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Numbers n such that p(2n) is prime, where p(n) is the number of partitions of n.
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%I #8 Aug 11 2019 05:26:04

%S 1,2,3,18,66,84,93,94,106,108,151,183,220,249,273,329,543,648,789,793,

%T 1068,1251,1254,1284,1366,1456,1549,1584,1671,1771,2059,2131,2228,

%U 2331,2501,3399,3729,4224,4456,4646,4999,5093,5540,6014,6510,6736,7520,8124

%N Numbers n such that p(2n) is prime, where p(n) is the number of partitions of n.

%C 2n-th partition number (A000041(2n)) is prime.

%H Max Alekseyev, <a href="/A114165/b114165.txt">Table of n, a(n) for n = 1..2451</a>

%t Select[ Range[9137], PrimeQ[ PartitionsP[2# ]] &]

%o (PARI) is(n)=isprime(numbpart(2*n)) \\ _Charles R Greathouse IV_, Feb 17 2017

%Y Cf. A000041, A046063, A068413, A114165, A111389, A111045, A114166, A111036, A114167, A114168, A114169, A114170.

%K nonn

%O 1,2

%A _Robert G. Wilson v_, Nov 14 2005