|
%I #9 Aug 23 2021 12:57:25
%S 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,
%T 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,
%U 21,5,5,7,7,2,9,5,10,11,10,7,8,3,3,14,4,7
%N 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.
%e 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)}.
%o (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
%Y Cf. A006530, A134835.
%K nonn
%O 1,1
%A _Leroy Quet_, Nov 12 2007
%E More terms from _Jinyuan Wang_, Aug 22 2021
|
