A002504 Numbers x such that 1 + 3*x*(x-1) is a ("cuban") prime (cf. A002407).
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
Keywords
Examples
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)
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
Programs
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Mathematica
Select[Range[500], PrimeQ[1 + 3 # (# - 1)] &] (* T. D. Noe, Jan 30 2013 *)
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PARI
for(k=1,999,isprime(3*k*(k-1)+1)&print1(k",")) \\ M. F. Hasler, Nov 28 2007
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)
Extensions
Edited, updated (1 is no longer regarded as a prime) and extended by M. F. Hasler, Nov 28 2007
Comments