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A064397
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Numbers n such that prime(n) + prime(n+1) is a square.
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14
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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
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OFFSET
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1,1
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LINKS
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Zak Seidov, Table of n, a(n) for n=1..1000
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EXAMPLE
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n=15: prime(15) = 47 and prime(16) = 53, 47 + 53 = 100 = 10^2.
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MATHEMATICA
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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 *)
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PROG
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(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
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CROSSREFS
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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
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KEYWORD
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nonn
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AUTHOR
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Jason Earls, Sep 29 2001
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STATUS
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approved
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