login

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”).

A125254
Smallest prime divisor of 4n-1 that is of the form 4k-1.
2
3, 7, 11, 3, 19, 23, 3, 31, 7, 3, 43, 47, 3, 11, 59, 3, 67, 71, 3, 79, 83, 3, 7, 19, 3, 103, 107, 3, 23, 7, 3, 127, 131, 3, 139, 11, 3, 151, 31, 3, 163, 167, 3, 7, 179, 3, 11, 191, 3, 199, 7, 3, 211, 43, 3, 223, 227, 3, 47, 239, 3, 19, 251, 3, 7, 263, 3, 271, 11, 3, 283, 7, 3, 59, 23
OFFSET
1,1
COMMENTS
4n-1 always has a prime divisor congruent to 3 modulo 4.
REFERENCES
T. M. Apostol, Introduction to Analytic Number Theory, Springer-Verlag, 1976, page 147.
EXAMPLE
The divisors of 4*9 - 1 = 35 are 5 and 7, so a(9) = 7.
MATHEMATICA
Table[SelectFirst[Transpose[FactorInteger[4n-1]][[1]], Mod[#, 4]==3&], {n, 80}] (* The program uses the SelectFirst function from Mathematica version 10 *) (* Harvey P. Dale, Mar 05 2015 *)
PROG
(PARI) vector(76, n, f=factor(4*n-1); r=0; until(f[r, 1]%4==3, r++); f[r, 1])
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Nick Hobson, Nov 26 2006
STATUS
approved