A100419 Numbers k such that 30*k+{1,7,13,17,19,23,29} are all prime.

89, 6627, 18674, 223949, 229269, 240007, 267356, 606681, 638454, 771496, 951060, 1068030, 1150693, 1254839, 1688923, 1920084, 2413577, 2433289, 2649414, 3053398, 3080572, 3337444, 3586658, 3604256, 3830335, 4137166

Offset

1,1

Comments

Values are 5 mod 7.

In each case, the 7 primes are necessarily consecutive. See the comment in A100418. - Peter Munn, Sep 06 2023

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..2020 from Robert Israel)

Maple

filter:= proc(n) local j; andmap(isprime, [seq(30*n+j, j=[1, 7, 13, 17, 19, 23, 29])]) end proc:
select(filter, [seq(i, i=5..5*10^6, 7)]); # Robert Israel, Nov 04 2024

Mathematica

Select[Range[42*10^5], AllTrue[30#+{1, 7, 13, 17, 19, 23, 29}, PrimeQ]&] (* The program uses the AllTrue function from Mathematica version 10 *) (* Harvey P. Dale, Mar 10 2018 *)

Prog

(Magma) [ n: n in [5..70000000 by 7] | forall{ q: q in [1, 7, 13, 17, 19, 23, 29] | IsPrime(30*n+q) } ]; // Klaus Brockhaus, Feb 24 2011

Crossrefs

Cf. A005776, A007775, A076205, A100418, A100420-A100423.

Sequence in context: A282478 A342049 A264323 * A328355 A264135 A264020

Adjacent sequences: A100416 A100417 A100418 * A100420 A100421 A100422

Keyword

nonn

Author

Ferenc Adorjan (fadorjan(AT)freemail.hu), Nov 19 2004

Extensions

Edited by Don Reble, Nov 17 2005

Status

approved