A133832 Least number k > n such that the binary trinomial 1 + 2^n + 2^k is prime, or 0 if there is no such k.

2, 3, 5, 13, 6, 7, 9, 9, 18, 19, 14, 13, 15, 17, 17, 81, 20, 19, 30, 33, 26, 27, 38, 81, 27, 35, 31, 33, 35, 31, 42, 458465, 36, 45, 47, 37, 67, 53, 41, 57, 42, 45, 46, 69, 54, 57, 53, 1009, 100, 119, 55, 73, 83, 67, 57, 1265, 74, 69, 66, 113, 75, 101, 66, 2241, 68, 67, 70

Offset

1,1

Comments

Conjecture: a(n) is nonzero for all n. These binary trinomials can also be written as f*2^n+1, where f=2^m+1 for some m, which is reminiscent of the Sierpinski problem (see A076336). The conjecture is equivalent to no Sierpinski numbers of the form 2^m+1 existing.

The PFGW program was used to find a(32), which produces a 138012-digit probable prime.

Links

T. D. Noe, Table of n, a(n) for n=1..255

Henri Lifchitz and Renaud Lifchitz (Editors), Search for 2^n+2^m+1, PRP Top Records.

Mathematica

mx=4000; Table[s=1+2^n; k=n+1; While[k<mx && !PrimeQ[s+2^k], k++ ]; If[k==mx, 0, k], {n, 100}]

Crossrefs

Cf. A057732, A059242, A057196, A057200, A081091 (various forms of prime binary trinomials).

Cf. A095056, A133830 (k < n equivalent), A133831.

Sequence in context: A108225 A259503 A193064 * A328997 A061488 A236394

Adjacent sequences: A133829 A133830 A133831 * A133833 A133834 A133835

Keyword

nonn

Author

T. D. Noe, Sep 26 2007

Extensions

Edited by Peter Munn, Sep 29 2024

Status

approved