WXML Winter 2017

Number Theory and Noise

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OIES iddescription sound player creator
A000069odious numbers: numbers with an odd number of 1's in their binary expansiondownloadEmily Flanagan
A000124quadratic sequence n(n+1)/2 + 1downloadEmily Flanagan
A000566heptagonal numbers (or 7-gonal numbers): n(5n-3)/2downloadEmily Flanagan
A005891centered pentagonal numbers: (5n^2+5n+2)/2downloadEmily Flanagan, Jesse Rivera
A005901quadratic sequence 10n^2 + 2downloadEmily Flanagan
A005905quadratic sequence 14n^2 + 2downloadEmily Flanagan
A005914quadratic sequence 12n^2 + 2downloadEmily Flanagan
A006446numbers n such that floor(sqrt(n)) divides ndownloadEmily Flanagan
A010003quadratic sequence 11n^2 + 2downloadEmily Flanagan
A010004quadratic sequence 13n^2 + 2downloadEmily Flanagan
A023254numbers that remain prime through 2 iterations of the function f(x) = 5x + 6downloadEmily Flanagan
A023255numbers that remain prime through 2 iterations of the function f(x) = 5x + 8downloadEmily Flanagan
A023256numbers that remain prime through 2 iterations of the function f(x) = 6x + 1downloadEmily Flanagan
A023257numbers that remain prime through 2 iterations of the function f(x) = 6x + 5downloadEmily Flanagan
A023258numbers that remain prime through 2 iterations of the function f(x) = 6x + 7downloadEmily Flanagan
A206399quadratic sequence 41n^2 + 2downloadEmily Flanagan
A2594863n^2 - 3n + 1 + 6 floor((n-1)(n-2)/6)downloadEmily Flanagan
A268037numbers n such that the number of divisors of n+2 divides n and the number of divisors of n divides n+2downloadEmily Flanagan
 
 
A000062 floor(n/(e-2)) downloadJesse Rivera
A001951 floor(n sqrt(2)) downloadJesse Rivera
A002473 numbers whose prime divisors are all <= 7 downloadJesse Rivera
A003136 numbers of the form x^2 + xy + y^2downloadJesse Rivera
A006218 sum of the number of divisors of k, k=1,...,n downloadJesse Rivera
A011257 geometric mean of phi(n) and sigma(n) is an integer downloadJesse Rivera
A022838 floor( n sqrt(3)) downloadJesse Rivera
A022839 floor(n sqrt(5)) downloadJesse Rivera
A022843 floor(n e) downloadJesse Rivera
A022844 floor(n pi) downloadJesse Rivera
A030513 numbers with four divisorsdownloadJesse Rivera
A030626 numbers with eight divisorsdownloadJesse Rivera
A036844 numbers divisible by the sum of their prime factorsdownloadJesse Rivera
A038152 floor(n e^pi) downloadJesse Rivera
A038153 floor(n pi^e)downloadJesse Rivera
A051913 numbers n such that phi(n)/phi(phi(n)) = 3 downloadJesse Rivera
A080683 numbers whose prime divisors are all <= 23 downloadJesse Rivera
A165350 primes p such that floor((p^2-1)/4)+p is not primedownloadJesse Rivera
A190751n+[ns/r]+[nt/r]+[nu/r]+[nv/r]+[nw/r], where r=sinh(x), s=cosh(x), t=tanh(x), u=csch(x), v=sech(x), w=coth(x), where x=pi/2downloadJesse Rivera
A252895numbers with an odd number of square divisorsdownloadJesse Rivera
A274685odd numbers n such that sigma(n) is divisible by 5downloadJesse Rivera
A277052n+floor(n/(2/sqrt(Pi)-1)) downloadJesse Rivera
 
 
A250046 numbers n such that m = floor(n/7) is coprime to n and, if nonzero, m is also a term of the sequence downloadPenny Espinoza
A250046 numbers n such that m = floor(n/7) is coprime to n and, if nonzero, m is also a term of the sequence (longer version)downloadPenny Espinoza
A250048 numbers n such that m = floor(n/6) is coprime to n and, if nonzero, m is also a term of the sequence downloadPenny Espinoza
A250050 numbers n such that m = floor(n/5) is coprime to n and, if nonzero, m is also a term of the sequence downloadPenny Espinoza
A250036 numbers n such that m = floor(n/4) is coprime to n and, if nonzero, m is also a term of the sequence downloadPenny Espinoza
A250038 numbers n such that m = floor(n/16) is coprime to n and, if nonzero, m is also a term of the sequence downloadPenny Espinoza
A250040 numbers n such that m = floor(n/10) is coprime to n and, if nonzero, m is also a term of the sequencedownloadPenny Espinoza
A250042 numbers n such that m = floor(n/9) is coprime to n and, if nonzero, m is also a term of the sequence downloadPenny Espinoza
A250044 numbers n such that m = floor(n/8) is coprime to n and, if nonzero, m is also a term of the sequence downloadPenny Espinoza
A161165 the n-th twin prime plus the n-th isolated prime downloadPenny Espinoza
A166251 isolated primes: primes p such that there is no other prime in the interval [2 prevprime(p/2), 2 nextprime(p/2)] downloadPenny Espinoza
A167706 single or isolated numbers: the union of single (or isolated or non-twin) primes and single (or isolated or average of twin prime pairs) nonprimes downloadPenny Espinoza
A167771 Twice-isolated primes: primes p such that neither p+-2 nor p+-4 is prime downloadPenny Espinoza
A065049Odd primes of incorrect parity: number of 1's in the binary representation of n (mod 2) equals 1 - (n mod 3) (mod 2). Also called isolated primes. downloadPenny Espinoza
A147778positive integers of the form u*v*(u^2-v^2) where u,v are co-prime integers downloadPenny Espinoza
A153777 minimal sequence S such that 1 is in S and if x is in S, then 5x-1 and 5x+1 are in S downloadPenny Espinoza
A153777 minimal sequence S such that 1 is in S and if x is in S, then 5x-1 and 5x+1 are in S (10 minute version: silence after 4:36) downloadPenny Espinoza
A003586 3-smooth numbers: numbers of the form 2^i 3^j with i, j >= 0downloadPenny Espinoza
A033845numbers of the form 2^i 3^j, with i,j >= 1 downloadPenny Espinoza
A052160 isolated prime difference equals 6: d(n)=p(n+1)-p(n)=6 but d(n+1) and d(n-1) differ from 6downloadPenny Espinoza
A001097twin primesdownloadPenny Espinoza
A007510 single, isolated or non-twin primes: primes p such that neither p-2 nor p+2 is primedownloadPenny Espinoza
A181732 numbers n such that 90n + 1 is prime downloadPenny Espinoza
A196000 numbers n such that 90n + 19 is prime downloadPenny Espinoza
A198382 numbers n such that 90n + 37 is prime downloadPenny Espinoza
A201734 numbers n such that 90n + 47 is prime downloadPenny Espinoza
A195993 numbers n such that 90n + 73 is prime downloadPenny Espinoza
A196007 numbers n such that 90n + 83 is prime downloadPenny Espinoza
A006450 prime-indexed primes: primes with prime subscripts downloadPenny Espinoza
A066643 floor(pi n^2) downloadPenny Espinoza
A018900Sum of digits in base 2 is 2 downloadPenny Espinoza
A226636Sum of digits in base 3 is 3 downloadPenny Espinoza
A226969Sum of digits in base 4 is 4 downloadPenny Espinoza
A227062Sum of digits in base 5 is 5 downloadPenny Espinoza
A227080Sum of digits in base 6 is 6 downloadPenny Espinoza
A227092Sum of digits in base 7 is 7 downloadPenny Espinoza
A227095Sum of digits in base 8 is 8 downloadPenny Espinoza
A227238Sum of digits in base 9 is 9 downloadPenny Espinoza
A052224Sum of digits in base 10 is 10 downloadPenny Espinoza
Sum of digits in base 55 equals 55 downloadPenny Espinoza

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