A134834 Let {b_n(m)} be a sequence defined by b_n(0)=1, b_n(m) is the largest prime dividing (b_n(m-1) + n). Then a(n) is the smallest positive integer such that b_n(m + a(n)) = b_n(m), for all integers m that are greater than some positive integer M.

2, 3, 2, 4, 3, 8, 2, 3, 4, 6, 2, 6, 3, 3, 2, 5, 4, 10, 3, 4, 3, 2, 2, 3, 3, 3, 8, 6, 8, 22, 2, 5, 5, 8, 2, 8, 4, 9, 2, 4, 3, 12, 3, 3, 6, 6, 2, 7, 4, 6, 3, 6, 4, 3, 3, 5, 12, 14, 3, 14, 4, 12, 3, 8, 6, 21, 5, 5, 7, 7, 2, 9, 5, 10, 11, 10, 7, 8, 3, 3, 14, 4, 7

Offset

1,1

Links

Table of n, a(n) for n=1..83.

Example

Sequence {b_9(m)} is 1, 5, 7, 2, 11, 5, 7, 2, 11, ... (5, 7, 2, 11) repeats. So a(9) = 4, the length of the cycle in {b_9(m)}.

Prog

(PARI) a(n) = my(b=1, k, v=List([1])); until(k<#v, k=1; listput(v, b=vecmax(factor(b+n)[, 1])); until(v[k]==b||k==#v, k++)); #v-k; \\ Jinyuan Wang, Aug 22 2021

Crossrefs

Cf. A006530, A134835.

Sequence in context: A378161 A261172 A374192 * A035583 A145178 A105079

Adjacent sequences: A134831 A134832 A134833 * A134835 A134836 A134837

Keyword

nonn

Author

Leroy Quet, Nov 12 2007

Extensions

More terms from Jinyuan Wang, Aug 22 2021

Status

approved