

A335898


a(n) = a(floor((n1)/a(n1))) + a(floor((n2)/a(n2))) with a(1) = a(2) = 1.


2



1, 1, 2, 2, 2, 2, 3, 3, 2, 3, 4, 3, 3, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 5, 5, 4, 5, 5, 4, 5, 6, 5, 5, 6, 5, 5, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 5, 6, 6, 4, 6, 6, 5, 6, 6, 6, 6, 6, 7, 6, 6, 8, 7, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 7, 7, 6, 7, 7, 6, 7
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OFFSET

1,3


COMMENTS

This sequence is a_1(n) where a_i(n) = Sum_{k=1..i+1} a_i(floor((nk)/a_i(nk))) with a_i(n) = 1 for n <= i+1.
Conjecture: This sequence hits every positive integer.


LINKS

Altug Alkan, Table of n, a(n) for n = 1..10000


MATHEMATICA

a[1] = a[2] = 1; a[n_] := a[n] = a[Floor[(n1)/a[n1]]] + a[Floor[(n2)/a[n2]]]; Array[a, 100] (* Amiram Eldar, Jun 29 2020 *)


PROG

(PARI) a=vector(10^2); a[1]=a[2]=1; for(n=3, #a, a[n]=a[(n1)\a[n1]]+a[(n2)\a[n2]]); a


CROSSREFS

Cf. A130535, A283207.
Sequence in context: A093450 A096198 A103183 * A143901 A115263 A055894
Adjacent sequences: A335895 A335896 A335897 * A335899 A335900 A335901


KEYWORD

nonn,look,easy


AUTHOR

Altug Alkan, following a suggestion from Andrew R. Booker, Jun 29 2020


STATUS

approved



