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A014753 Primes p==1 (mod 6) such that 3 and -3 are both cubes (one implies other) modulo p. 5
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 (list; graph; refs; listen; history; text; internal format)
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

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 * A316933 A255225 A141167

Adjacent sequences:  A014750 A014751 A014752 * A014754 A014755 A014756

KEYWORD

nonn

AUTHOR

Warren D. Smith

EXTENSIONS

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

STATUS

approved

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Last modified February 16 20:45 EST 2019. Contains 320189 sequences. (Running on oeis4.)