A125254 Smallest prime divisor of 4n-1 that is of the form 4k-1.

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.

Links

Nick Hobson, Table of n, a(n) for n = 1..1000

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

Cf. A057205, A111863, A125255.

Sequence in context: A042775 A229596 A125255 * A093931 A335980 A153788

Adjacent sequences: A125251 A125252 A125253 * A125255 A125256 A125257

Keyword

easy,nonn

Author

Nick Hobson, Nov 26 2006

Status

approved