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A233393
Primes of the form 2^k - 1 + q(m) with k > 0 and m > 0, where q(.) is the strict partition function (A000009).
7
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
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}]
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Dec 08 2013
STATUS
approved