

A258153


Numbers of the form p^2 + q with p, q and 2*p + 3 all prime.


1



6, 7, 9, 11, 15, 17, 21, 23, 27, 28, 30, 32, 33, 35, 36, 38, 41, 42, 44, 45, 47, 48, 51, 52, 54, 56, 57, 60, 62, 63, 65, 66, 68, 71, 72, 75, 77, 78, 80, 83, 84, 86, 87, 90, 92, 93, 96, 98, 101, 102, 104, 105, 107, 108, 110, 111, 113, 114, 116, 117, 120, 122, 126, 128, 131, 132, 134, 135, 138, 141
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OFFSET

1,1


COMMENTS

The conjecture in A258141 asserts that any six consecutive positive integers contain at least a term of the current sequence.


LINKS

ZhiWei Sun, Table of n, a(n) for n = 1..10000


EXAMPLE

a(1) = 6 since 6 = 2^2 + 2 with 2 and 2*2+3 = 7 both prime.
a(2) = 7 since 7 = 2^2 + 3 with 2, 3, 2*2+3 all prime.


MATHEMATICA

n=0; Do[Do[If[PrimeQ[2Prime[k]+3]&&PrimeQ[mPrime[k]^2], n=n+1; Print[n, " ", m]; Goto[aa]], {k, 1, PrimePi[Sqrt[m]]}];
Label[aa]; Continue, {m, 1, 141}]


CROSSREFS

Cf. A000040, A023204, A258139, A258140, A258141.
Sequence in context: A022892 A120164 A074898 * A175221 A094010 A100348
Adjacent sequences: A258150 A258151 A258152 * A258154 A258155 A258156


KEYWORD

nonn


AUTHOR

ZhiWei Sun, May 22 2015


STATUS

approved



