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A002504
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Numbers x such that 1 + 3*x*(x-1) is a ("cuban") prime (cf. A002407).
(Formerly M0522 N0188)
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8
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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
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OFFSET
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1,1
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COMMENTS
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Equivalently, positive integers x such that x^3 - (x-1)^3 is prime. - Rémi Guillaume, Oct 24 2023
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REFERENCES
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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).
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LINKS
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FORMULA
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a(n) = ceiling(sqrt(A002407(n)/3)).
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EXAMPLE
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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)
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MATHEMATICA
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Select[Range[500], PrimeQ[1 + 3 # (# - 1)] &] (* T. D. Noe, Jan 30 2013 *)
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PROG
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(PARI) for(k=1, 999, isprime(3*k*(k-1)+1)&print1(k", ")) \\ M. F. Hasler, Nov 28 2007
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Edited, updated (1 is no longer regarded as a prime) and extended by M. F. Hasler, Nov 28 2007
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STATUS
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approved
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