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A261542 Integers k such that k^2 + 1 = 2*p where p and p+2 are twin primes. 1
3, 9, 51, 69, 231, 279, 309, 471, 519, 579, 639, 699, 819, 861, 909, 1029, 1311, 1419, 1629, 1701, 1749, 1899, 2151, 2541, 2619, 2799, 3201, 3291, 3429, 3501, 3981, 4089, 4719, 4809, 4941, 5061, 5301, 5571, 5679, 5739, 5859, 6369, 6621, 6789, 6939, 7071, 7149 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

The corresponding primes p are 5, 41, 1301, 2381, 26681, 38921, 47741, 110921, 134681, ... and are in A001359 (lesser of twin primes).

Property of the sequence: the primes p > 5 are congruent to 41 mod 180 => a(n)^2 == 9, 81 mod 180 for n>1.

LINKS

Robert Israel, Table of n, a(n) for n = 1..10000

EXAMPLE

3 is in the sequence because 3^2 + 1 = 2*5 and 2 + 5 = 7 is prime.

MAPLE

with(numtheory):

  for n from 1 by 2 to 8000 do:

     p:=n^2+1:

     if isprime(p/2) and isprime(p/2+2)

     then

     printf(`%d, `, n):

     else

     fi:

  od:

CROSSREFS

Cf. A002522, A001359.

Sequence in context: A036751 A260156 A058110 * A171951 A323232 A319105

Adjacent sequences:  A261539 A261540 A261541 * A261543 A261544 A261545

KEYWORD

nonn

AUTHOR

Michel Lagneau, Aug 24 2015

STATUS

approved

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Last modified January 20 05:20 EST 2020. Contains 331067 sequences. (Running on oeis4.)