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

Author

Nick Hobson, Nov 26 2006

Keywords

• easy
• nonn

Comments

4n-1 always has a prime divisor congruent to 3 modulo 4.

Examples

			The divisors of 4*9 - 1 = 35 are 5 and 7, so a(9) = 7.
		

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

Crossrefs

Cf. A057205, A111863, A125255.

Programs

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 *)

PARI

vector(76, n, f=factor(4*n-1); r=0; until(f[r,1]%4==3, r++); f[r,1])