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A088264 Smallest number k > 0 such that prefixing k to the n-th quadruple in the set {(1,3,7,9), (11,13,17,19), (21,23,27,29), ...} yields all primes.

%I A088264 #16 Jun 19 2017 03:30:49
%S A088264 1,189,8,94,156,32,34,18,14,1,1653,101,2764,99,326,715,144,1322,4300,
%T A088264 768,122,67,72,500,427,3,77,22,285,119,25,294,632,55,51,3974,217,1230,
%U A088264 1022,346,1461,260,19,9,536,463,3,299,1,69,539,1285,1833,116,397,3951
%N A088264 Smallest number k > 0 such that prefixing k to the n-th quadruple in the set {(1,3,7,9), (11,13,17,19), (21,23,27,29), ...} yields all primes.
%C A088264 a(n) is the least k such that 10^A055642(n)*k+n is in A007811. - _Robert Israel_, Jun 18 2017
%H A088264 Robert Israel, <a href="/A088264/b088264.txt">Table of n, a(n) for n = 1..10000</a>
%e A088264 a(2) = 189 as 189 is the smallest number such that 18911, 18913, 18917 and 18919 are all prime.
%p A088264 f:= proc(n) local R,k,p;
%p A088264 R:= map(`+`,[1,3,7,9],10*(n-1));
%p A088264 p:= 10^(ilog10(R[1])+1);
%p A088264 for k from 1 do
%p A088264   if map(t -> isprime(t+p*k), R) = [true,true,true,true] then return k fi
%p A088264 od
%p A088264 end proc:
%p A088264 map(f, [$1..60]); # _Robert Israel_, Jun 18 2017
%Y A088264 Cf. A007530, A007811, A055642.
%K A088264 base,nonn
%O A088264 1,2
%A A088264 _Amarnath Murthy_, Sep 28 2003
%E A088264 Corrected and extended by _Ray G. Opao_, Mar 23 2005
%E A088264 More terms from _David Wasserman_, Jul 27 2005