A216299 - OEIS

A216299

Numbers k such that 10k+1 is composite but 10k+3, 10k+7, 10k+9 are all prime.

22, 61, 85, 142, 166, 169, 178, 199, 268, 316, 415, 451, 478, 541, 682, 775, 787, 862, 1045, 1111, 1237, 1387, 1618, 1720, 1738, 2014, 2035, 2074, 2131, 2215, 2305, 2362, 2410, 2710, 2773, 2938, 3013, 3055, 3271, 3334, 3361, 3412, 3652, 4012, 4042, 4069

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OFFSET

1,1

LINKS

V. Raman, Table of n, a(n) for n = 1..10000

FORMULA

a(n) >> n log^3 n. - Charles R Greathouse IV, Sep 07 2012

MATHEMATICA

t = {}; Do[ps = Select[Range[10*n, 10*n + 9], PrimeQ]; If[ps == {10*n + 3, 10*n + 7, 10*n + 9}, AppendTo[t, n]], {n, 0, 4978}]; t (* T. D. Noe, Sep 03 2012 *)

Select[Range[4100], CompositeQ[10#+1]&&AllTrue[10#+{3, 7, 9}, PrimeQ]&] (* Requires Mathematica version 10 or later *) (* Harvey P. Dale, Sep 14 2019 *)

PROG

(Magma) [k:k in [1..4100]| not IsPrime(10*k+1) and forall{m:m in [3, 7, 9]| IsPrime(10*k+m)}]; // Marius A. Burtea, Feb 02 2020

CROSSREFS

Cf. A032352, A007811, A078494.

Sequence in context: A044124 A044505 A156797 * A255431 A221595 A051874

Adjacent sequences: A216296 A216297 A216298 * A216300 A216301 A216302

KEYWORD

nonn

AUTHOR

V. Raman, Sep 03 2012

STATUS

approved