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%I #24 Sep 08 2022 08:45:04
%S 7,15,20,61,152,190,293,377,492,558,789,919,942,1768,2343,2429,2693,
%T 2952,3136,3720,4837,5421,5722,6870,7347,8126,8193,9465,9857,9927,
%U 10410,10483,10653,12685,13763,13955,16033,16342,17859,18367,18474
%N Numbers n such that prime(n) + prime(n+1) is a square.
%H Zak Seidov, <a href="/A064397/b064397.txt">Table of n, a(n) for n=1..1000</a>
%e n=15: prime(15) = 47 and prime(16) = 53, 47 + 53 = 100 = 10^2.
%t lst={};Do[p1=Prime[n];p2=Prime[n+1];q=(p1+p2)^0.5;If[q==IntegerPart[q], AppendTo[lst, n]], {n, 1, 9!}];lst (* _Vladimir Joseph Stephan Orlovsky_, Sep 02 2008 *)
%o (PARI) j=[]; for(n=1,30000,x=prime(n)+prime(n+1); if(issquare(x),j=concat(j,n))); j
%o (PARI) { n=0; default(primelimit, 8500000); for (m=1, 10^9, if (issquare(prime(m) + prime(m + 1)), write("b064397.txt", n++, " ", m); if (n==175, break)) ) } \\ _Harry J. Smith_, Sep 13 2009
%o (Magma) [n: n in [0..50000]| IsSquare(NthPrime(n) +NthPrime(n+1))]; // _Vincenzo Librandi_, Apr 06 2011
%Y Cf. A061275 (the primes), A062703 (squares), A074924 (square root of sum).
%Y Cf. A076305 (3 primes), A072849 (4 primes), A166255 (70 primes), A166261 (120 primes).
%K nonn
%O 1,1
%A _Jason Earls_, Sep 29 2001
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