Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).
%I M0522 N0188 #63 Feb 22 2024 13:34:13
%S 2,3,4,5,7,10,11,12,14,15,18,24,25,26,28,29,31,33,35,38,39,42,43,46,
%T 49,50,53,56,59,63,64,67,68,75,81,82,87,89,91,92,94,96,106,109,120,
%U 124,126,129,130,137,141,143,148,154,157,158,159,165,166,171,172
%N Numbers x such that 1 + 3*x*(x-1) is a ("cuban") prime (cf. A002407).
%C Equivalently, positive integers x such that x^3 - (x-1)^3 is prime. - _Rémi Guillaume_, Oct 24 2023
%D A. J. C. Cunningham, On quasi-Mersennian numbers, Mess. Math., 41 (1912), 119-146.
%D N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
%D N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
%H T. D. Noe, <a href="/A002504/b002504.txt">Table of n, a(n) for n = 1..1000</a>
%F From _Rémi Guillaume_, Dec 07 2023: (Start)
%F a(n) = ceiling(sqrt(A002407(n)/3)).
%F a(n) = A111251(n) + 1.
%F a(n) = (A121259(n) + 1)/2. (End)
%e From _Rémi Guillaume_, Dec 07 2023: (Start)
%e 1 + 3*7*6 = 127 = A002407(5) is the 5th prime of this form, so a(5) = 7.
%e 1 + 3*10*9 = 271 = A002407(6) is the 6th prime of this form, so a(6) = 10.
%e (End)
%t Select[Range[500], PrimeQ[1 + 3 # (# - 1)] &] (* _T. D. Noe_, Jan 30 2013 *)
%o (PARI) for(k=1,999,isprime(3*k*(k-1)+1)&print1(k",")) \\ _M. F. Hasler_, Nov 28 2007
%Y Cf. A002407 (resulting primes), A111251, A121259.
%K nonn
%O 1,1
%A _N. J. A. Sloane_
%E Edited, updated (1 is no longer regarded as a prime) and extended by _M. F. Hasler_, Nov 28 2007