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

Author

Amarnath Murthy, Jun 03 2003

Keywords

• nonn

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

Examples

			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.
		

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)

Crossrefs

Cf. A113767, A192580.

Programs

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 *)

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