A002504 Numbers x such that 1 + 3*x*(x-1) is a ("cuban") prime (cf. A002407). (Formerly M0522 N0188)

2, 3, 4, 5, 7, 10, 11, 12, 14, 15, 18, 24, 25, 26, 28, 29, 31, 33, 35, 38, 39, 42, 43, 46, 49, 50, 53, 56, 59, 63, 64, 67, 68, 75, 81, 82, 87, 89, 91, 92, 94, 96, 106, 109, 120, 124, 126, 129, 130, 137, 141, 143, 148, 154, 157, 158, 159, 165, 166, 171, 172

Offset

1,1

Comments

Equivalently, positive integers x such that x^3 - (x-1)^3 is prime. - Rémi Guillaume, Oct 24 2023

References

A. J. C. Cunningham, On quasi-Mersennian numbers, Mess. Math., 41 (1912), 119-146.

N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

Links

T. D. Noe, Table of n, a(n) for n = 1..1000

Formula

From Rémi Guillaume, Dec 07 2023: (Start)

a(n) = ceiling(sqrt(A002407(n)/3)).

a(n) = A111251(n) + 1.

a(n) = (A121259(n) + 1)/2. (End)

Example

From Rémi Guillaume, Dec 07 2023: (Start)
1 + 3*7*6 = 127 = A002407(5) is the 5th prime of this form, so a(5) = 7.
1 + 3*10*9 = 271 = A002407(6) is the 6th prime of this form, so a(6) = 10.
(End)

Mathematica

Select[Range[500], PrimeQ[1 + 3 # (# - 1)] &] (* T. D. Noe, Jan 30 2013 *)

Prog

(PARI) for(k=1, 999, isprime(3*k*(k-1)+1)&print1(k", ")) \\ M. F. Hasler, Nov 28 2007

Crossrefs

Cf. A002407 (resulting primes), A111251, A121259.

Sequence in context: A356311 A117092 A285276 * A133431 A305705 A123091

Adjacent sequences: A002501 A002502 A002503 * A002505 A002506 A002507

Keyword

nonn

Author

N. J. A. Sloane

Extensions

Edited, updated (1 is no longer regarded as a prime) and extended by M. F. Hasler, Nov 28 2007

Status

approved