A055496 a(1) = 2; a(n) is smallest prime > 2*a(n-1).

2, 5, 11, 23, 47, 97, 197, 397, 797, 1597, 3203, 6421, 12853, 25717, 51437, 102877, 205759, 411527, 823117, 1646237, 3292489, 6584983, 13169977, 26339969, 52679969, 105359939, 210719881, 421439783, 842879579, 1685759167, 3371518343

Offset: 1

Author

N. J. A. Sloane, Jul 07 2000

Keywords

• nonn

Comments

It appears that lim_{n->infinity} a(n)/2^n exists and is approximately 1.569985585.... - Franklin T. Adams-Watters, Nov 11 2011

This is a B_2 sequence. - Thomas Ordowski, Sep 23 2014 See the link.

Conjecture: lim_{n->infinity} a(n)/A006992(n) = 5.1648264... - Thomas Ordowski, Apr 05 2015

Links

• Zak Seidov and Michael De Vlieger, Table of n, a(n) for n = 1..1000 (First 100 terms from Zak Seidov)
• V. Shevelev, Ramanujan and Labos primes, their generalizations, and classifications of primes, J. Integer Seq. 15 (2012), #12.5.4.
• Eric Weisstein's World of Mathematics, B_2-Sequence.

Crossrefs

Cf. A006992, A060264, A163963.

Values of a(n)-2*a(n-1) in A163469. - Zak Seidov, Jul 28 2009

Cf. A065545 (with a(1)=3). - Zak Seidov, Feb 04 2016

Row 1 of A229608.

Programs

Maple

A055496 := proc(n) option remember; if n=1 then 2 else nextprime(2*A055496(n-1)); fi; end;

Mathematica

NextPrim[n_Integer] := Block[ {k = n + 1}, While[ !PrimeQ[k], k++ ]; Return[k]]; a[1] = 2; a[n_] := NextPrim[ 2*a[n - 1]]; Table[ a[n], {n, 1, 31} ]
a[1]=2;a[n_]:=a[n]=Prime[PrimePi[2*a[n-1]]+1];Table[a[n],{n,40}] (* Zak Seidov, Feb 16 2006 *)
NestList[ NextPrime[2*# ]&,2,100] (* Zak Seidov, Jul 28 2009 *)

PARI

print1(a=2);for(n=2,20,print1(", ",a=nextprime(a+a))) \\ Charles R Greathouse IV, Jul 19 2011

Formula

a(n+1) = A060264(a(n)). - Peter Munn, Oct 23 2017

Extensions

Mathematica updated by Jean-François Alcover, Jun 19 2013