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Numbers k such that prime(k) + prime(k+1)*2 is a square.
1

%I #25 Apr 13 2024 14:57:50

%S 9,96,461,548,565,876,1053,1202,1302,1426,1596,2040,3040,4392,5710,

%T 6960,7749,7988,8630,8818,9323,9505,10465,11617,11828,12674,13119,

%U 17580,18507,18954,22922,23197,25821,33502,35877,37065,37321

%N Numbers k such that prime(k) + prime(k+1)*2 is a square.

%H Harry J. Smith, <a href="/A064504/b064504.txt">Table of n, a(n) for n = 1..175</a>

%t okQ[list_]:=IntegerQ[Sqrt[First[list]+2Last[list]]];

%t PrimePi/@Transpose[Select[Partition[Prime[Range[40000]],2,1],okQ]][[1]]

%t (* _Harvey P. Dale_, Mar 05 2011 *)

%o (PARI) for(n=1,10^6, if(issquare(prime(n)+prime(n+1)*2),print1(n," ")))

%o (PARI) { n=0; default(primelimit, 21000000); for (m=1, 10^9, if (issquare(prime(m) + 2*prime(m + 1)), write("b064504.txt", n++, " ", m); if (n==175, break)) ) } \\ _Harry J. Smith_, Sep 16 2009

%K nonn

%O 1,1

%A _Jason Earls_, Oct 06 2001

%E Offset changed from 0 to 1 by _Harry J. Smith_, Sep 16 2009