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

1,1

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)

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

Example

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

Maple

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

Prog

(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

Crossrefs

Cf. A007528, A016969, A024898, A107745.

Sequence in context: A314241 A314242 A107745 * A333656 A043389 A277571

Adjacent sequences: A111860 A111861 A111862 * A111864 A111865 A111866

Keyword

nonn,look

Author

Reinhard Zumkeller, Aug 20 2005

Status

approved