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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
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
KEYWORD
nonn
AUTHOR
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.)