OFFSET

1,1

COMMENTS

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?

EXAMPLE

(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.

(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.

MATHEMATICA

Select[Prime[Range[300]], If[IntegerQ[(#^2+Prime[PrimePi[ # ]+1]^2)/10], PrimeQ[(#^2+Prime[PrimePi[ # ]+1]^2)/10]]&]

Transpose[Select[Partition[Prime[Range[300]], 2, 1], PrimeQ[Total[ #^2]/10]&]] [[1]] (* Harvey P. Dale, Dec 15 2011 *)

CROSSREFS

KEYWORD

nonn

AUTHOR

J. M. Bergot, Jun 04 2007

EXTENSIONS

Edited and extended by Stefan Steinerberger, Jun 14 2007

STATUS

approved