A100422 - OEIS

%I #23 Sep 06 2023 11:49:10

%S 1,53887,114731,123306,139742,210554,471745,480859,619039,630862,

%T 858929,1075873,1306614,1714945,1913514,2767458,3014285,3454137,

%U 3518243,3699151,3864512,3874291,4274376,4862362,4878329,4937822

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

%C Values are 1 mod 7.

%C In each case, the 7 primes are necessarily consecutive. See the comment in A100418. - _Peter Munn_, Sep 06 2023

%p a:= proc(n) option remember;

%p       local m;

%p       if n=1 then 1

%p       else for m from 30*(a(n-1)+7) by 210

%p            while not (isprime (m+1) and isprime (m+7) and

%p                  isprime (m+11) and isprime (m+13) and

%p                  isprime (m+17) and isprime (m+23) and

%p                  isprime (m+29))

%p            do od; m/30

%p         fi

%p     end:

%p seq (a(n), n=1..10);

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

%o (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 Cf. A005776, A007775, A076205, A100418-A100423.

%K easy,nonn

%O 1,2

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

%E Edited by _Don Reble_, Nov 17 2005