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%I #16 Apr 17 2020 02:50:53
%S 17,23,13,13,41,1627,37,17,73,431,89,37,23,571,199,41,137,211,349,941,
%T 13729,41299,19259,313,5309,1031,42409,2797,53,6211,13339,17,43759,47,
%U 491,13,787,139787,13,89,21937,29947,3449,24533,8839,18979,619,2713,23
%N Lesser of two consecutive primes such that p + n*q is a perfect square, p < q.
%H Harry J. Smith, <a href="/A064543/b064543.txt">Table of n, a(n) for n = 1..100</a>
%t Do[ k = 1; While[ ! IntegerQ[ Sqrt[ Prime[ k ] + n*Prime[ k + 1 ] ] ], k++ ]; Print[ Prime[ k ] ], {n, 1, 182} ]
%o (PARI) ps(n, k) = prime(n)+k*prime(n+1) k=1; for(n=1,10^6, if(issquare(ps(n,k)),print1(prime(n)," "); k++; n=0))
%o (PARI) ps(m, n)= { prime(m) + n*prime(m + 1) }
%o { n=0; default(primelimit, 4000000); for (n=1, 100, m=1; while (!issquare(ps(m, n)), m++); write("b064543.txt", n, " ", prime(m)) ) } \\ _Harry J. Smith_, Sep 18 2009
%Y Cf. A064545.
%K nonn
%O 1,1
%A _Jason Earls_, Oct 08 2001
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