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%I #20 Jan 19 2014 00:11:37
%S 0,3981186,146202480,1165139284,2002776304,5677052574,9441118506,
%T 13199287564,14655461200,21663769144,23911959136,28132616434,
%U 29959257966,34716681516,35619315204,35690387094,38966503234,42887165056,45425679640,47063988520,51444908350,53558122980
%N Numbers k such that (k^i)+7 for 1<=i<=7 are seven prime numbers.
%C Conjecture: the sequence is infinite.
%e 0 is in the sequence since (0^i)+7 = 7 is prime for i>0.
%e 3981186 is in the sequence because the following seven numbers are primes: 3981186+7, 3981186^2+7, ..., 3981186^7+7.
%o (Java)
%o import java.math.*;
%o public class A234798 {
%o public static void main (String[] args) {
%o BigInteger c7 = BigInteger.valueOf(7);
%o for (long i=0; ; i+=2) {
%o if (!BigInteger.valueOf(i+7).isProbablePrime(80))
%o continue;
%o BigInteger bi = BigInteger.valueOf(i), b=bi;
%o long k;
%o for (k=1; k<7; ++k) {
%o b = b.multiply(bi);
%o if (!b.add(c7).isProbablePrime(80)) break;
%o }
%o if (k==7) System.out.printf("%d, ", i);
%o }
%o }
%o }
%Y Cf. A000040.
%K nonn,hard
%O 1,2
%A _Alex Ratushnyak_, Dec 30 2013
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