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

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

1,2

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.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Mathematica

NestList[If[PrimeQ[#], 2#, #+1]&, 1, 50] (* Harvey P. Dale, Aug 26 2013 *)

Prog

(PARI) u=1; for(n=2, 100, v=if(isprime(u), u+1, 2*u); u=v; print1(v, ", "))

Crossrefs

Cf. A163962, A055496.

Sequence in context: A128216 A299322 A365501 * A091856 A083416 A022770

Adjacent sequences: A080732 A080733 A080734 * A080736 A080737 A080738

Keyword

nonn

Author

Benoit Cloitre, Mar 08 2003

Status

approved