

A002504


Numbers x such that 1 + 3*x*(x1) 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  (x1)^3 is prime.  Rémi Guillaume, Oct 24 2023


REFERENCES

A. J. C. Cunningham, On quasiMersennian numbers, Mess. Math., 41 (1912), 119146.
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

a(n) = ceiling(sqrt(A002407(n)/3)).


EXAMPLE

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*(k1)+1)&print1(k", ")) \\ M. F. Hasler, Nov 28 2007


CROSSREFS



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



