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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: 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

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Last modified July 9 09:40 EDT 2020. Contains 335542 sequences. (Running on oeis4.)