A129899 Smaller member p of a pair of consecutive primes (p,q) such that p^2 + q^2 is ten times a prime number.

7, 11, 19, 23, 31, 41, 61, 67, 83, 89, 101, 107, 127, 131, 173, 197, 263, 271, 277, 311, 353, 359, 373, 379, 389, 461, 467, 521, 653, 683, 719, 797, 827, 929, 967, 991, 997, 1061, 1069, 1163, 1181, 1201, 1231, 1277, 1291, 1307, 1447, 1451, 1453, 1487, 1553

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?

Links

Table of n, a(n) for n=1..51.

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

Sequence in context: A329857 A168489 A329979 * A129842 A065312 A343142

Adjacent sequences: A129896 A129897 A129898 * A129900 A129901 A129902

Keyword

nonn

Author

J. M. Bergot, Jun 04 2007

Extensions

Edited and extended by Stefan Steinerberger, Jun 14 2007

Status

approved