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A111863
a(n) is the smallest prime factor of 6*n-1 that is congruent to 5 modulo 6.
5
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
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
KEYWORD
nonn,look
AUTHOR
Reinhard Zumkeller, Aug 20 2005
STATUS
approved