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%I #16 Sep 20 2018 00:31:31
%S 409,599,739,911,1217,1481,3539,3637,4421,5081,7591,7951,10301,10993,
%T 11173,14449,14533,15619,16073,16453,17203,17341,18661,21319,22259,
%U 23671,23869,26267,27059,30169,32119,33409,35531,37139,39511,41411,42193,42641,45979,46171,47741,55931,58937,60761,65089,70991,79867,80599,84389,86579,90523,96739,98909,100913,104717,105199,108343,112573,122263,123551,129581,136951,156419
%N Primes p such that q^2 - p^2 + 1 is the square of a composite number where p and q are consecutive primes.
%C Calculations provided by Robert Israel.
%C For what p will the number of squared prime be less than the number of squared composites? What would the distribution be for increasing p?
%e With p=409 and q=419, 419^2 - 409^2 + 1 = 8281 = 91^2.
%t Select[Partition[Prime@ Range[10^4], 2, 1], CompositeQ@ Sqrt[#2^2 - #1^2 + 1] & @@ # &][[All, 1]] (* _Michael De Vlieger_, Jul 19 2018 *)
%Y Cf. A000040, A157750.
%K nonn
%O 1,1
%A _J. M. Bergot_, Jul 16 2018