A084435 a(1) = 2, then smallest prime of the form 2^k*a(n-1) + 1.

2, 3, 7, 29, 59, 1889, 3779, 7559, 4058207223809, 32465657790473, 4462046030502692971872257, 9582170887127842377060195852353537

Offset

1,1

Comments

This sequence also is generated when the initial term is 1. It is unclear if the sequence is finite or infinite. - Bob Selcoe, Oct 09 2015

References

Donald E. Knuth, The Art of Computer Programming, Vol. 2, Seminumerical Algorithms, problem 39, page 76.

Links

Robert G. Wilson v, Table of n, a(n) for n = 1..15 (shortened by N. J. A. Sloane, Jan 13 2019)

Example

a(3)=7 because 3*2+1=7 is prime;
a(4)=29 because 7*2+1=15 is not prime, 7*4+1=29 is prime.

Mathematica

f[s_List] := Block[{k = 0, p = s[[-1]]}, While[q = 2^k*p + 1; !PrimeQ[ q], k++]; Append[s, q]]; s = {2}; Nest[f, s, 16] (* Robert G. Wilson v, Mar 11 2015 *)

Prog

(PARI) lista(nn) = {a = 2; print1(a, ", "); for (n=1, nn, k=0; while (!isprime(2^k*a+1), k++); a = 2^k*a+1; print1(a, ", "); ); } \\ Michel Marcus, Mar 18 2015

Crossrefs

Cf. A113767, A192580.

Sequence in context: A062573 A019435 A061092 * A072469 A004062 A037151

Adjacent sequences: A084432 A084433 A084434 * A084436 A084437 A084438

Keyword

nonn

Author

Amarnath Murthy, Jun 03 2003

Status

approved