OFFSET

1,4

COMMENTS

A variation of the Hofstadter-Conway $10,000 sequence (A004001). See antisymmetric humps (between its generational boundaries) of a(n) - n/2 in Links section. More precisely, the k-th generation of this sequence begins at 3*2^(k-3) + 2 for k > 2. Similar sequences can be created by generalized recurrence a_i(n) = a_i(a_i(n-1)) + a_i(n-a_i(n-i)) with i + 1 initial conditions a_i(1) = a_i(2) = ... = a_i(i+1) = 1. See also an illustration about this sequence family for i <= 10 in Links section.

LINKS

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

Altug Alkan, Scatterplots of a_i(n)-n/2 for i <= 10 and n <= 10^5

Altug Alkan, On a conjecture about generalized Q-recurrence, Open Mathematics (2018) Vol. 16, Issue 1, 1490-1500.

MATHEMATICA

Fold[Append[#1, #1[[#1[[#2 - 1]] ]] + #1[[#2 - #1[[#2 - 2]] ]] ] &, {1, 1, 1}, Range[4, 85]] (* Michael De Vlieger, Dec 22 2017 *)

PROG

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

CROSSREFS

KEYWORD

nonn,easy

AUTHOR

Altug Alkan, Dec 21 2017

STATUS

approved