A014753 Primes p==1 (mod 6) such that 3 and -3 are both cubes (one implies other) modulo p.

61, 67, 73, 103, 151, 193, 271, 307, 367, 439, 499, 523, 547, 577, 613, 619, 643, 661, 727, 757, 787, 853, 919, 967, 991, 997, 1009, 1021, 1093, 1117, 1249, 1303, 1321, 1399, 1531, 1543, 1549, 1597, 1609, 1621, 1669, 1759, 1783, 1861, 1867

Offset

1,1

Comments

Primes of the form x^2+xy+61y^2, whose discriminant is -243. - T. D. Noe, May 17 2005

Primes of the form (x^2 + 243*y^2)/4. - Arkadiusz Wesolowski, May 30 2015

References

K. Ireland and M. Rosen, A classical introduction to modern number theory, Vol. 84, Graduate Texts in Mathematics, Springer-Verlag. Exercise 23, p. 135.

Links

Bruno Berselli, Table of n, a(n) for n = 1..1000

Mathematica

p6 = Select[6*Range[0, 400]+1, PrimeQ]; Select[p6, (Reduce[3 == k^3+m*#, {k, m}, Integers] =!= False)&] (* Jean-François Alcover, Feb 20 2014 *)

Prog

(PARI) forprime(p=1, 9999, p%6==1&&ispower(Mod(3, p), 3)&&print1(p", ")) \\ M. F. Hasler, Feb 18 2014
(PARI) is_A014753(p)={p%6==1&&ispower(Mod(3, p), 3)&&isprime(p)} \\ M. F. Hasler, Feb 18 2014

Crossrefs

Cf. A014752, A014755.

Sequence in context: A295157 A095575 A095563 * A349461 A316933 A255225

Adjacent sequences: A014750 A014751 A014752 * A014754 A014755 A014756

Keyword

nonn,easy

Author

Warren D. Smith

Extensions

Offset changed from 0 to 1 by Bruno Berselli, Feb 20 2014

Status

approved