A233393 Primes of the form 2^k - 1 + q(m) with k > 0 and m > 0, where q(.) is the strict partition function (A000009).

2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 37, 41, 43, 47, 53, 61, 67, 71, 73, 79, 83, 101, 107, 109, 127, 131, 137, 139, 149, 157, 167, 173, 181, 191, 193, 199, 223, 229, 257, 263, 269, 271, 277, 293, 311, 331, 347, 349, 359, 383, 397, 421, 449, 463, 467, 479, 521, 523, 557, 587

Offset

1,1

Comments

Conjecture: The sequence has infinitely many terms.

This follows from the conjecture in A233390.

Links

Zhi-Wei Sun, Table of n, a(n) for n = 1..542

Z.-W. Sun, On a^n+ bn modulo m, arXiv preprint arXiv:1312.1166 [math.NT], 2013-2014.

Example

a(1) = 2 since 2^1 - 1 + q(1) = 1 + 1 = 2.
a(2) = 3 since 2^1 - 1 + q(3) = 1 + 2 = 3.
a(3) = 5 since 2^2 - 1 + q(3) = 3 + 2 = 5.

Mathematica

Pow[n_]:=Pow[n]=Mod[n, 2]==0&&2^(IntegerExponent[n, 2])==n
n=0
Do[Do[If[Pow[Prime[m]-PartitionsQ[k]+1],
n=n+1; Print[n, " ", Prime[m]]; Goto[aa]]; If[PartitionsQ[k]>=Prime[m], Goto[aa]]; Continue, {k, 1, 2*Prime[m]}];
Label[aa]; Continue, {m, 1, 110}]

Crossrefs

Cf. A000040, A000225, A232504, A233307, A233346, A233359, A233360, A233390.

Sequence in context: A100110 A095323 A100370 * A233265 A095319 A129621

Adjacent sequences: A233390 A233391 A233392 * A233394 A233395 A233396

Keyword

nonn

Author

Zhi-Wei Sun, Dec 08 2013

Status

approved