A258153 Numbers of the form p^2 + q with p, q and 2*p + 3 all prime.

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

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

Zhi-Wei 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[m-Prime[k]^2], n=n+1; Print[n, " ", m]; Goto[aa]], {k, 1, PrimePi[Sqrt[m]]}];
Label[aa]; Continue, {m, 1, 141}]
Module[{pp=40}, Select[Union[#[[1]]^2+#[[2]]&/@Select[Tuples[ Prime[ Range[ pp]], 2], PrimeQ[2#[[1]]+3]&]], #<=Prime[pp]-4&]] (* Harvey P. Dale, Jul 24 2021 *)

Crossrefs

Cf. A000040, A023204, A258139, A258140, A258141.

Sequence in context: A120164 A335623 A074898 * A175221 A094010 A100348

Adjacent sequences: A258150 A258151 A258152 * A258154 A258155 A258156

Keyword

nonn

Author

Zhi-Wei Sun, May 22 2015

Status

approved