cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A080735 a(1)=1, then a(n)=2*a(n-1) if a(n-1) is prime, a(n)=a(n-1)+1 otherwise.

Original entry on oeis.org

1, 2, 4, 5, 10, 11, 22, 23, 46, 47, 94, 95, 96, 97, 194, 195, 196, 197, 394, 395, 396, 397, 794, 795, 796, 797, 1594, 1595, 1596, 1597, 3194, 3195, 3196, 3197, 3198, 3199, 3200, 3201, 3202, 3203, 6406, 6407, 6408, 6409, 6410, 6411, 6412, 6413, 6414, 6415, 6416
Offset: 1

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Author

Benoit Cloitre, Mar 08 2003

Keywords

Comments

Conjectures: (Strong) Let x,y be 2 positive integers and define a(n) as a(1)=1, a(n)=x*a(n-1) if a(n-1) is prime, a(n)=a(n-1)+y otherwise; then lim_{n->oo} log(a(n))/sqrt(n) = C(x,y) exists. (Weak) log(a(n))/sqrt(n) is bounded.

Crossrefs

Programs

  • Mathematica
    NestList[If[PrimeQ[#],2#,#+1]&,1,50] (* Harvey P. Dale, Aug 26 2013 *)
  • PARI
    u=1; for(n=2,100,v=if(isprime(u),u+1,2*u); u=v; print1(v,","))

Formula

It seems that log(a(n))/sqrt(n) -> C, a constant around 1.3.....
a(n) = A055496(m) when a(n+1) > a(n) + 1. - Bill McEachen, Mar 24 2024
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