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%I #13 Nov 21 2013 12:49:04
%S 7,11,19,23,31,41,61,67,83,89,101,107,127,131,173,197,263,271,277,311,
%T 353,359,373,379,389,461,467,521,653,683,719,797,827,929,967,991,997,
%U 1061,1069,1163,1181,1201,1231,1277,1291,1307,1447,1451,1453,1487,1553
%N Smaller member p of a pair of consecutive primes (p,q) such that p^2 + q^2 is ten times a prime number.
%C How many prime numbers p have a consecutive prime q such that p^2 + q^2 has 10 as a divisor? What is the density of those numbers among the primes?
%e (7,11) is a pair of consecutive prime numbers. Since 7^2+11^2 = 10*17, where 17 is prime, 7 is in the sequence.
%e (13,17) is also a pair of consecutive prime numbers but 13^2 + 17^2 = 458 is not ten times a prime number. Hence 13 is not in the sequence.
%t Select[Prime[Range[300]], If[IntegerQ[(#^2+Prime[PrimePi[ # ]+1]^2)/10], PrimeQ[(#^2+Prime[PrimePi[ # ]+1]^2)/10]]&]
%t Transpose[Select[Partition[Prime[Range[300]],2,1],PrimeQ[Total[ #^2]/10]&]] [[1]] (* _Harvey P. Dale_, Dec 15 2011 *)
%K nonn
%O 1,1
%A _J. M. Bergot_, Jun 04 2007
%E Edited and extended by _Stefan Steinerberger_, Jun 14 2007
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