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A125821 Numbers n for which 8n+5 and 8n+7 are twin primes. 7
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 13 20:38 EDT 2019. Contains 327981 sequences. (Running on oeis4.)