A236390 Positive integers m with 2^m*p(m) + 1 prime, where p(.) is the partition function (A000041).

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

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}]
Select[Range[40000], PrimeQ[2^# PartitionsP[#]+1]&] (* Harvey P. Dale, Dec 30 2020 *)

Crossrefs

Cf. A000040, A000041, A236389.

Sequence in context: A063191 A329167 A216976 * A048464 A075824 A228951

Adjacent sequences: A236387 A236388 A236389 * A236391 A236392 A236393

Keyword

nonn

Author

Zhi-Wei Sun, Jan 24 2014

Status

approved