A317442 a(1) = a(2) = 1; for n >= 3, a(n) = a(t(n)) + a(n-t(n)) where t = A000195.

1, 1, 2, 3, 4, 5, 6, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11, 11, 12, 12, 13, 14, 14, 15, 16, 16, 17, 18, 18, 19, 20, 20, 21, 22, 22, 23, 24, 24, 25, 26, 26, 27, 28, 28, 29, 30, 30, 31, 32, 32, 33, 34, 34, 35, 36, 37, 37, 38, 39, 40, 40, 41, 42, 43, 43, 44, 45, 46, 46, 47, 48, 49, 49, 50, 51, 52

Offset

1,3

Comments

This sequence hits every positive integer.

Links

Table of n, a(n) for n=1..76.

Altug Alkan, A log plot of a(n)/n

Formula

a(n+1) - a(n) = 0 or 1 for all n >= 1.

Mathematica

Nest[Function[{a, n}, Append[a, a[[Floor@ Log@ n]] + a[[n - Floor@ Log@ n]] ] ] @@ {#, Length@ # + 1} &, {1, 1}, 74] (* Michael De Vlieger, Jul 30 2018 *)

Prog

(PARI) q=vector(100); for(n=1, 2, q[n]=1); for(n=3, #q, q[n]=q[floor(log(n))] + q[n-floor(log(n))]); q

Crossrefs

Cf. A000195, A316434.

Sequence in context: A327706 A121856 A332061 * A132172 A080680 A005376

Adjacent sequences: A317439 A317440 A317441 * A317443 A317444 A317445

Keyword

nonn

Author

Altug Alkan, Jul 28 2018

Status

approved