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 A064397 Numbers n such that prime(n) + prime(n+1) is a square. 14
 7, 15, 20, 61, 152, 190, 293, 377, 492, 558, 789, 919, 942, 1768, 2343, 2429, 2693, 2952, 3136, 3720, 4837, 5421, 5722, 6870, 7347, 8126, 8193, 9465, 9857, 9927, 10410, 10483, 10653, 12685, 13763, 13955, 16033, 16342, 17859, 18367, 18474 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 LINKS Zak Seidov, Table of n, a(n) for n=1..1000 EXAMPLE n=15: prime(15) = 47 and prime(16) = 53, 47 + 53 = 100 = 10^2. MATHEMATICA 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 *) PROG (PARI) j=[]; for(n=1, 30000, x=prime(n)+prime(n+1); if(issquare(x), j=concat(j, n))); j (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 (Magma) [n: n in [0..50000]| IsSquare(NthPrime(n) +NthPrime(n+1))]; // Vincenzo Librandi, Apr 06 2011 CROSSREFS Cf. A061275 (the primes), A062703 (squares), A074924 (square root of sum). Cf. A076305 (3 primes), A072849 (4 primes), A166255 (70 primes), A166261 (120 primes). Sequence in context: A298050 A115783 A140109 * A214467 A151971 A014659 Adjacent sequences: A064394 A064395 A064396 * A064398 A064399 A064400 KEYWORD nonn AUTHOR Jason Earls, Sep 29 2001 STATUS approved

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Last modified March 29 20:41 EDT 2023. Contains 361599 sequences. (Running on oeis4.)