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

%I A100422 #23 Sep 06 2023 11:49:10
%S A100422 1,53887,114731,123306,139742,210554,471745,480859,619039,630862,
%T A100422 858929,1075873,1306614,1714945,1913514,2767458,3014285,3454137,
%U A100422 3518243,3699151,3864512,3874291,4274376,4862362,4878329,4937822
%N A100422 Numbers n such that 30*n+{1,7,11,13,17,23,29} are all prime.
%C A100422 Values are 1 mod 7.
%C A100422 In each case, the 7 primes are necessarily consecutive. See the comment in A100418. - _Peter Munn_, Sep 06 2023
%p A100422 a:= proc(n) option remember;
%p A100422       local m;
%p A100422       if n=1 then 1
%p A100422       else for m from 30*(a(n-1)+7) by 210
%p A100422            while not (isprime (m+1) and isprime (m+7) and
%p A100422                  isprime (m+11) and isprime (m+13) and
%p A100422                  isprime (m+17) and isprime (m+23) and
%p A100422                  isprime (m+29))
%p A100422            do od; m/30
%p A100422         fi
%p A100422     end:
%p A100422 seq (a(n), n=1..10);
%t A100422 Select[Range[5000000],And@@PrimeQ/@(30(#)+{1,7,11,13,17,23,29})&]  (* _Harvey P. Dale_, Feb 23 2011 *)
%o A100422 (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
%Y A100422 Cf. A005776, A007775, A076205, A100418-A100423.
%K A100422 easy,nonn
%O A100422 1,2
%A A100422 Ferenc Adorjan (fadorjan(AT)freemail.hu), Nov 19 2004
%E A100422 Edited by _Don Reble_, Nov 17 2005