The OEIS Foundation is supported by donations from users of the OEIS and by a grant from the Simons Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A309027 Prime powers of the form 12*c^2 + 4*c + 3, c 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS It is conjectured that all terms are actually primes. See Leung et al. p. 12. All terms up to 10^9 are primes. 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 LINKS Ka Hin Leung, Koji Momihara, 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*n-8) && (d=sqrtint(3*n-8)) && ((frac((d-1)/6) == 0) || (frac((d+1)/6) == 0)); CROSSREFS Sequence in context: A163183 A007520 A294912 * A213891 A163851 A213051 Adjacent sequences:  A309024 A309025 A309026 * A309028 A309029 A309030 KEYWORD nonn AUTHOR Michel Marcus, Jul 08 2019 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified February 25 08:15 EST 2020. Contains 332221 sequences. (Running on oeis4.)