A125821 Numbers n for which 8n+5 and 8n+7 are twin primes.

3, 12, 18, 24, 33, 57, 102, 132, 153, 159, 162, 234, 243, 249, 267, 279, 288, 297, 318, 348, 423, 432, 444, 447, 477, 489, 519, 528, 552, 564, 579, 627, 684, 687, 717, 774, 783, 837, 858, 918, 948, 969, 984, 993

Offset

1,1

Comments

Proof that all numbers in this sequence are divisible by 3 (Zak Seidov Apr 19 2008:

if n=(3k+1), then 8n+7=8(3k+1)+7=3(5+8 k) (composite)

if n=(3k+2), then 8n+5=8(3k+2)+5=3(7+8 k) (composite),

so if we require that both 8n+5 and 8n+7 are primes, then n=3k, hence all terms in A125821 are multiples of 3. QED.

Links

Harvey P. Dale, Table of n, a(n) for n = 1..1000

Mathematica

Do[If[PrimeQ[8n + 5] && PrimeQ[8n + 7], Print[n]], {n, 1, 1000}]
Select[Range[3, 6000, 3], AllTrue[8#+{5, 7}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Sep 14 2018 *)

Crossrefs

Cf. A001109.

For a(n)/3 see A139404.

Cf. A125822, A139402, A139404.

Sequence in context: A032703 A234904 A284806 * A239052 A063229 A061564

Adjacent sequences: A125818 A125819 A125820 * A125822 A125823 A125824

Keyword

nonn

Author

Artur Jasinski, Dec 10 2006

Status

approved