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 A002504 Numbers x such that 1 + 3*x*(x-1) is a ("cuban") prime (cf. A002407). (Formerly M0522 N0188) 8
 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 (list; graph; refs; listen; history; text; internal format)
 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

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Last modified April 16 21:54 EDT 2024. Contains 371755 sequences. (Running on oeis4.)