A105120 a(1) = 2; k(1) = 0; for n > 1: k(n) = smallest number j >= k(n-1) such that 2*a(n-1) + j is prime; a(n) = 2*a(n-1) + k(n).

2, 5, 11, 23, 47, 97, 197, 397, 797, 1597, 3203, 6421, 12889, 25841, 51749, 103567, 207227, 414553, 829211, 1658533, 3317177, 6634469, 13269059, 26538257, 53076679, 106153547, 212307299, 424614829, 849229907, 1698460067, 3396920419

Offset: 1

Author

Yasutoshi Kohmoto, Apr 08 2005

Keywords

• nonn

Comments

Numbers k(n) are given in A105121.

a(n) appears to tend toward C*A055496(n), C~ 0.992521946129820000. - Bill McEachen, Feb 21 2022

Examples

			a(10) = 1597; k(10) = 3; 2*1597 + j is not prime for 3 <= j < 9, but 2*1597 + 9 = 3203 is prime. Hence k(11) = 9 and a(11) = 3203.
		

Links

• Robert G. Wilson v, Table of n, a(n) for n = 1..3000..

Crossrefs

k(n) is in A105121.

Programs

Mathematica

a[1] = {2, 0}; a[n_] := a[n] = Block[{m = 2a[n - 1][[1]], k = a[n - 1][[2]]}, While[ !PrimeQ[m + k], k++ ]; {m + k, k}]; Table[ a[n][[1]], {n, 30}] (* Robert G. Wilson v, Apr 08 2005 *)

PARI

print1(a=2,","); k=0; for(n=2,31, j=k; while(!isprime(2*a+j),j++); k=j; print1(a=2*a+k,",")) \\ Klaus Brockhaus, Apr 08 2005

Extensions

Edited, corrected and extended by Klaus Brockhaus and Robert G. Wilson v, Apr 08 2005