A271723 -id:A271723 - cp's OEIS frontend

A309027 Prime powers of the form 12c^2 + 4c + 3, where c is an arbitrary integer.

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

Offset: 1

Michel Marcus, Jul 08 2019

nonn

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

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.

Cf. A271723.

isok(n) = isprimepower(n) && issquare(3*n-8) && (d=sqrtint(3*n-8)) && ((frac((d-1)/6) == 0) || (frac((d+1)/6) == 0));

cp's OEIS Frontend

A309027 Prime powers of the form 12c^2 + 4c + 3, where c is an arbitrary integer.

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cp's OEIS Frontend

A309027 Prime powers of the form 12*c^2 + 4*c + 3, where c is an arbitrary integer.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

PARI

A309027 Prime powers of the form 12c^2 + 4c + 3, where c is an arbitrary integer.