A296816 a(n) = a(a(n-1)) + a(n-a(n-2)) with a(1) = a(2) = a(3) = 1.

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

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(n)-n/2 and A004001(n)-n/2 for n <= 10^5

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

Cf. A004001, A005229.

Sequence in context: A051134 A347777 A037458 * A064474 A379067 A072688

Adjacent sequences: A296813 A296814 A296815 * A296817 A296818 A296819

Keyword

nonn,easy

Author

Altug Alkan, Dec 21 2017

Status

approved