A100422 Numbers n such that 30*n+{1,7,11,13,17,23,29} are all prime.

1, 53887, 114731, 123306, 139742, 210554, 471745, 480859, 619039, 630862, 858929, 1075873, 1306614, 1714945, 1913514, 2767458, 3014285, 3454137, 3518243, 3699151, 3864512, 3874291, 4274376, 4862362, 4878329, 4937822

Offset

1,2

Comments

Values are 1 mod 7.

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

Links

Table of n, a(n) for n=1..26.

Maple

a:= proc(n) option remember;
      local m;
      if n=1 then 1
      else for m from 30*(a(n-1)+7) by 210
           while not (isprime (m+1) and isprime (m+7) and
                 isprime (m+11) and isprime (m+13) and
                 isprime (m+17) and isprime (m+23) and
                 isprime (m+29))
           do od; m/30
        fi
    end:
seq (a(n), n=1..10);

Mathematica

Select[Range[5000000], And@@PrimeQ/@(30(#)+{1, 7, 11, 13, 17, 23, 29})&]  (* Harvey P. Dale, Feb 23 2011 *)

Prog

(Magma) [ n: n in [0..5000000] | forall{ q: q in [1, 7, 11, 13, 17, 23, 29] | IsPrime(30*n+q) } ]; // Klaus Brockhaus, Feb 23 2011

Crossrefs

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

Sequence in context: A252035 A099231 A237547 * A099010 A164723 A164720

Adjacent sequences: A100419 A100420 A100421 * A100423 A100424 A100425

Keyword

easy,nonn

Author

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

Extensions

Edited by Don Reble, Nov 17 2005

Status

approved