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Smaller of two consecutive primes whose sum is a square.
17

%I #22 Jun 28 2024 04:24:24

%S 17,47,71,283,881,1151,1913,2591,3527,4049,6047,7193,7433,15137,20807,

%T 21617,24197,26903,28793,34847,46817,53129,56443,69191,74489,83231,

%U 84047,98563,103049,103967,109507,110441,112337,136237,149057,151247

%N Smaller of two consecutive primes whose sum is a square.

%H Amiram Eldar, <a href="/A061275/b061275.txt">Table of n, a(n) for n = 1..10000</a> (terms 1..1000 from Harry J. Smith)

%F a(n) = A000040(A064397(n)). - _Amiram Eldar_, Jun 28 2024

%e a(4) = 283, the next prime is 293 and 283 + 293 = 576 = 24^2.

%t Transpose[Select[Partition[Prime[Range[20000]],2,1],IntegerQ[Sqrt[Plus@@# ]]&]][[1]] (* _Harvey P. Dale_, Aug 04 2009 *)

%o (PARI) { default(primelimit, 550655327); n=0; q=2; forprime (p=3, 550655327, if (issquare(p+q), write("b061275.txt", n++, " ", q)); q=p ) } \\ _Harry J. Smith_, Jul 20 2009

%Y Subset of A091624.

%Y Cf. A000040, A064397, A206279, A206280, A206281.

%K nonn,easy

%O 1,1

%A _Amarnath Murthy_, Apr 25 2001

%E More terms from Larry Reeves (larryr(AT)acm.org) and _Asher Auel_, May 15 2001

%E Offset changed from 0 to 1 by _Harry J. Smith_, Jul 20 2009