A283207 -id:A283207 - cp's OEIS frontend

A335898 a(n) = a(floor((n-1)/a(n-1))) + a(floor((n-2)/a(n-2))) with a(1) = a(2) = 1.

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

Offset: 1

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

This sequence is a_1(n) where a_i(n) = Sum_{k=1..i+1} a_i(floor((n-k)/a_i(n-k))) with a_i(n) = 1 for n <= i+1.

Conjecture: This sequence hits every positive integer.

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

Cf. A130535, A283207.

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

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

A335901 a(n) = 2*a(floor((n-1)/a(n-1))) with a(1) = 1.

Original entry on oeis.org

1, 2, 2, 2, 4, 2, 4, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 8, 4, 8, 4, 4, 4, 4, 4, 8, 4, 8, 4, 4, 4, 4, 4, 8, 4, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 4, 8, 4, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 4, 8, 4, 8, 4, 8, 4, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8

Offset: 1

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

Least k such that a(k) = 2^n are 1, 2, 5, 21, 169, 2705, ... (Conjecture: This sequence is A117261).

Robert Israel, Table of n, a(n) for n = 1..10000

Cf. A130147, A132424, A130535, A283207, A288914, A335898.

f:= proc(n) option remember;
  2*procname(floor((n-1)/procname(n-1))) end proc:
f(1):= 1:
map(f, [$1..105]); # Robert Israel, Jul 08 2020

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

a=vector(10^3); a[1]=1; for(n=2, #a, a[n]=2*a[(n-1)\a[n-1]]); a

A335855 a(n) = a(a(n-1)) + a(floor(n/a(n-1))) with a(1) = a(2) = a(3) = a(4) = 2.

Original entry on oeis.org

2, 2, 2, 2, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 4, 6, 6, 6, 6, 6, 6, 6, 6, 6, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 6, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8, 8

Offset: 1

Altug Alkan, Jun 27 2020

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

Cf. A004001, A283207.

a[1] = a[2] = a[3] = a[4] = 2; a[n_] := a[n] = a[a[n-1]] + a[Floor[n / a[n-1]]]; Array[a, 100] (* Amiram Eldar, Jun 27 2020 *)

a=vector(10^2); a[1]=a[2]=a[3]=a[4]=2; for(n=5, #a, a[n]=a[n\a[n-1]]+a[a[n-1]]); a

cp's OEIS Frontend

A335898 a(n) = a(floor((n-1)/a(n-1))) + a(floor((n-2)/a(n-2))) with a(1) = a(2) = 1.

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A335901 a(n) = 2*a(floor((n-1)/a(n-1))) with a(1) = 1.

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A335855 a(n) = a(a(n-1)) + a(floor(n/a(n-1))) with a(1) = a(2) = a(3) = a(4) = 2.

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