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
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Dec 08 2013
STATUS
approved