A064397 Numbers k such that prime(k) + prime(k+1) is a square.

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

Offset

1,1

Links

Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Zak Seidov)

Formula

a(n) = A000720(A061275(n)). - Amiram Eldar, Jun 28 2024

Example

For k=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), A000720.

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