

A309027


Prime powers of the form 12*c^2 + 4*c + 3, where c is an arbitrary integer.


0



3, 11, 19, 43, 59, 179, 211, 283, 563, 619, 739, 1163, 1499, 1979, 2083, 2411, 3011, 3539, 4259, 4723, 7603, 8011, 8219, 10211, 11411, 12163, 14011, 14563, 14843, 17483, 20011, 23059, 25579, 26699, 28619, 29803, 30203, 33923, 36083, 36523, 41539, 49411, 54139, 55219, 55763, 59083
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OFFSET

1,1


COMMENTS

It is conjectured that all terms are prime. See Leung et al. p. 12.
All terms up to 10^9 are prime.
Since the Diophantine equation 12*c^2 + 4*c + 3 = x^2 has no solution, all terms p^e have either e=1 or e>=3 and odd. Up to 10^24, all terms are prime.  Giovanni Resta, Jul 08 2019
It appears that these are the primes of A271723.  Bill McEachen, Aug 14 2021


LINKS

Table of n, a(n) for n=1..46.
Ka Hin Leung, Koji Momihara and Qing Xiang, A new family of Hadamard matrices of order 4(2q^2+1), arXiv:1907.02623 [math.CO], 2019. See p. 3.


PROG

(PARI) isok(n) = isprimepower(n) && issquare(3*n8) && (d=sqrtint(3*n8)) && ((frac((d1)/6) == 0)  (frac((d+1)/6) == 0));


CROSSREFS

Cf. A271723.
Sequence in context: A163183 A007520 A294912 * A213891 A336790 A163851
Adjacent sequences: A309024 A309025 A309026 * A309028 A309029 A309030


KEYWORD

nonn


AUTHOR

Michel Marcus, Jul 08 2019


STATUS

approved



