A111863 a(n) is the smallest prime factor of 6*n-1 that is congruent to 5 modulo 6.

5, 11, 17, 23, 29, 5, 41, 47, 53, 59, 5, 71, 11, 83, 89, 5, 101, 107, 113, 17, 5, 131, 137, 11, 149, 5, 23, 167, 173, 179, 5, 191, 197, 29, 11, 5, 17, 227, 233, 239, 5, 251, 257, 263, 269, 5, 281, 41, 293, 23, 5, 311, 317, 17, 47, 5, 11, 347, 353, 359, 5, 53, 29, 383, 389, 5

Offset: 1

Author

Reinhard Zumkeller, Aug 20 2005

Keywords

• nonn
• look

Comments

From Robert Israel, Jan 18 2023: (Start)

a(n) = 5 if n == 1 (mod 5).

a(n) = 6*n - 1 if n is in A024898. (End)

Examples

			For n = 13, 6*n - 1 = 77 = 7*11; 7 == 1 (mod 6), but 11 == 5 (mod 6), so a(13) = 11.
		

References

• G. Pólya and G. Szegő, Problems and Theorems in Analysis I (Springer 1924, reprinted 1972), Part Eight, Chap. 2, Section 2, Problem 96.

Links

• Robert Israel, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A007528, A016969, A024898, A107745.

Programs

Maple

f:= n -> min(select(p -> p mod 6 = 5, numtheory:-factorset(6*n-1))):
map(f, [$1..100]); # Robert Israel, Jan 18 2023

PARI

for(k=1,60,my(f=factor(6*k-1)[,1]);for(j=1,#f,if(f[j]%6==5,print1(f[j],", ");break))) \\ Hugo Pfoertner, Dec 25 2019