A290130 Numbers n > 0 such that either 3n+4, n-2, n+2, n+4 or 3n+5, n-1, n+1, n+5 are all primes.

6, 9, 12, 18, 42, 69, 102, 312, 348, 459, 642, 858, 1089, 1302, 1428, 1482, 1665, 2139, 2238, 2685, 2688, 3255, 3462, 3465, 3528, 3849, 4002, 4788, 5415, 6825, 7755, 7875, 8862, 9009, 9435, 10458, 11115, 11172, 11778, 11829, 13005, 13692, 14628, 18045, 19422, 19992, 21018, 21315, 21558

Offset

1,1

Comments

In all cases a is multiple of 3, c = a + 3 and b = a + 1 or 2.

First triples are: {6, 8, 9}, {9, 10, 12}, {12, 14, 15}, {18, 20, 21}, {42, 44, 45}, {69, 70, 72}, {102, 104, 105}, {312, 314, 315}, {348, 350, 351}, {459, 460, 462}, {642, 644, 645}, {858, 860, 861}.

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Maple

filter:= proc(n) if n::even then andmap(isprime, [3*n+5, n+5, n+1, n-1]) else andmap(isprime, [3*n+4, n+4, n+2, n-2]) fi end proc:
select(filter, [seq(i, i=3..30000, 3)]); # Robert Israel, Aug 01 2017

Mathematica

s = {}; Do[If[b + c > a && a + b > c && a + c > b && PrimeQ[a + b + c] && PrimeQ[-a + b + c] && PrimeQ[a - b + c] && PrimeQ[a + b - c], AppendTo[s, a}]], {a, 1000}, {b, a + 1, a + 2}, {c, b + 1, a+3}]; s
apQ[n_]:=AllTrue[{3n+4, n-2, n+2, n+4}, PrimeQ]||AllTrue[{3n+5, n-1, n+1, n+5}, PrimeQ]; Select[Range[22000], apQ] (* Harvey P. Dale, Nov 08 2024 *)

Crossrefs

Sequence in context: A315959 A023386 A036999 * A118782 A246356 A335065

Adjacent sequences: A290127 A290128 A290129 * A290131 A290132 A290133

Keyword

nonn

Author

N. J. A. Sloane, Jul 20 2017

Extensions

Definition simplified by Robert Israel, Aug 01 2017

Status

approved