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A234530
Primes p with q(p) + 1 also prime, where q(.) is the strict partition function (A000009).
14
2, 3, 11, 13, 29, 37, 47, 71, 79, 89, 103, 127, 131, 179, 181, 197, 233, 271, 331, 379, 499, 677, 691, 757, 887, 911, 1019, 1063, 1123, 1279, 1429, 1531, 1559, 1637, 2251, 2719, 3571, 4007, 4201, 4211, 4297, 4447, 4651, 4967, 5953, 6131, 7937, 8233, 8599, 8819, 9013, 11003, 11093, 11813, 12251, 12889, 12953, 13487, 13687, 15259
OFFSET
1,1
COMMENTS
By the conjecture in A234514, this sequence should have infinitely many terms.
It seems that a(n+1) < a(n) + a(n-1) for all n > 4.
See A234366 for primes of the form q(p) + 1 with p prime.
See also A234644 for a similar sequence.
LINKS
EXAMPLE
a(1) = 2 since 2 and q(2) + 1 = 2 are both prime.
a(2) = 3 since 3 and q(3) + 1 = 3 are both prime.
a(3) = 11 since 11 and q(11) + 1 = 13 are both prime.
MATHEMATICA
n=0; Do[If[PrimeQ[PartitionsQ[Prime[k]]+1], n=n+1; Print[n, " ", Prime[k]]], {k, 1, 10^5}]
Select[Prime[Range[2000]], PrimeQ[PartitionsQ[#]+1]&] (* Harvey P. Dale, Apr 23 2017 *)
KEYWORD
nonn
AUTHOR
Zhi-Wei Sun, Dec 27 2013
STATUS
approved