A083005 a(1)=1, a(n)=2a(n-1)+1 if a(n-1) is prime, a(n)=a(n-1)+1 otherwise.

1, 2, 5, 11, 23, 47, 95, 96, 97, 195, 196, 197, 395, 396, 397, 795, 796, 797, 1595, 1596, 1597, 3195, 3196, 3197, 3198, 3199, 3200, 3201, 3202, 3203, 6407, 6408, 6409, 6410, 6411, 6412, 6413, 6414, 6415, 6416, 6417, 6418, 6419, 6420, 6421, 12843, 12844

Offset: 1

Author

Benoit Cloitre, May 31 2003

Keywords

• nonn

Comments

Primes in this sequence are A055496.- Robert Israel, May 23 2017

Links

• Robert Israel, Table of n, a(n) for n = 1..10197

Crossrefs

Cf. A055496.

Programs

Maple

P[0]:= 0:
for n from 2 to 20 do P[n]:= nextprime(2*P[n-1]) od:
seq($2*P[i]+1..P[i+1],i=0..19); # Robert Israel, May 23 2017

Mathematica

NestList[If[PrimeQ[#],2#+1,#+1]&,1,50] (* Harvey P. Dale, Jul 02 2021 *)

Formula

Conjecture : limit n ->oo log(a(n))/sqrt(n)=c= 1.3....

Extensions

Offset corrected by Robert Israel, May 23 2017