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A129899 Smaller member p of a pair of consecutive primes (p,q) such that p^2 + q^2 is ten times a prime number. 0
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 19 09:35 EDT 2021. Contains 347556 sequences. (Running on oeis4.)