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A236390 Positive integers m with 2^m*p(m) + 1 prime, where p(.) is the partition function (A000041). 3
1, 9, 11, 15, 34, 36, 43, 80, 152, 159, 168, 200, 205, 354, 402, 957, 1898, 2519, 2729, 2932, 3075, 3740, 4985, 5839, 7911, 9868, 10210, 24624, 27735, 31553, 37190 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

According to the conjecture in A236389, this sequence should have infinitely many terms.

The prime 2^(a(31))*p(a(31)) + 1 = 2^(37190)*p(37190) + 1 has 11405 decimal digits.

LINKS

Zhi-Wei Sun, Table of n, a(n) for n = 1..31

EXAMPLE

a(1) = 1 since 2^1*p(1) + 1 = 2*1 + 1 = 3 is prime.

MATHEMATICA

q[n_]:=PrimeQ[2^n*PartitionsP[n]+1]

n=0; Do[If[q[m], n=n+1; Print[n, " ", m]], {m, 1, 10000}]

CROSSREFS

Cf. A000040, A000041, A236389.

Sequence in context: A027694 A063191 A216976 * A048464 A075824 A228951

Adjacent sequences:  A236387 A236388 A236389 * A236391 A236392 A236393

KEYWORD

nonn

AUTHOR

Zhi-Wei Sun, Jan 24 2014

STATUS

approved

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Last modified September 17 08:31 EDT 2019. Contains 327127 sequences. (Running on oeis4.)