A275163 -id:A275163 - cp's OEIS frontend

A278066 Relative of Hofstadter Q-sequence: a(1) = 5, a(2) = 2; thereafter a(n) = a(n-a(n-1)) + a(n-a(n-2)).

5, 2, 5, 2, 5, 7, 2, 12, 2, 12, 2, 12, 7, 4, 14, 14, 10, 14, 7, 14, 6, 26, 10, 4, 20, 33, 2, 33, 2, 33, 2, 33, 2, 38, 2, 38, 2, 38, 7, 4, 40, 40, 10, 40, 7, 14, 6, 78, 10, 4, 46, 85, 2, 85, 2, 85, 2, 85, 2, 85, 2, 85, 2, 85, 2, 85, 2, 85, 2, 85, 2, 85, 2, 85, 2, 85, 2

Offset: 1

Nathan Fox, Nov 13 2016

nonn

In calculating terms of this sequence, use the convention that a(n)=0 for n<=0.

Most terms in this sequence alternate between 2 and a term of A275163. These runs are separated by 18 other terms, and each run is approximately twice as long as the previous.

Nathan Fox, Table of n, a(n) for n = 1..10000
Nathan Fox, Hofstadter-like Sequences over Nonstandard Integers", Talk given at the Rutgers Experimental Mathematics Seminar, November 10 2016.

Cf. A005185, A275163, A278067, A278068.

a[1] = 5; a[2] = 2; a[n_] := a[n] = If[n < 1, 0, a[n-a[n-1]] + a[n-a[n-2]]];
Array[a, 100] (* Paolo Xausa, May 30 2024 *)

a(1) = 5, a(2) = 2, a(3) = 5, a(4) = 2, a(5) = 5, a(6) = 7, a(7) = 2; thereafter, for k>=0,
a(A275163(k)+1)=A275163(k)+5
a(A275163(k)+2)=2
a(A275163(k)+3)=A275163(k)+5
a(A275163(k)+4)=2
a(A275163(k)+5)=A275163(k)+5
a(A275163(k)+6)=7
a(A275163(k)+7)=4
a(A275163(k)+8)=A275163(k)+7
a(A275163(k)+9)=A275163(k)+7
a(A275163(k)+10)=10
a(A275163(k)+11)=A275163(k)+7
a(A275163(k)+12)=7
a(A275163(k)+13)=14
a(A275163(k)+14)=6
a(A275163(k)+15)=2*A275163(k)+12
a(A275163(k)+16)=10
a(A275163(k)+17)=4
a(A275163(k)+18)=A275163(k)+13
a(A275163(k)+i)=A275163(k+1), i odd, 19<=i<A275163(k+1)-A275163(k)
a(A275163(k)+i)=2, i odd, 20<=i<=A275163(k+1)-A275163(k).

A278068 Relative of Hofstadter Q-sequence: a(1) = 57, a(2) = 2; thereafter a(n) = a(n-a(n-1)) + a(n-a(n-2)).

Original entry on oeis.org

57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 2, 57, 59, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116, 2, 116

Offset: 1

Nathan Fox, Nov 13 2016

nonn

In calculating terms of this sequence, use the convention that a(n)=0 for n<=0.

This sequence is eventually, beginning with a(3128), quasilinear with quasiperiod 1402.

Nathan Fox, Table of n, a(n) for n = 1..10000
Nathan Fox, Hofstadter-like Sequences over Nonstandard Integers", Talk given at the Rutgers Experimental Mathematics Seminar, November 10 2016.
Nathan Fox, Formula for a(n)

Cf. A005185, A275163, A278066, A278067.

a[1] = 57; a[2] = 2; a[n_] := a[n] = If[n < 1, 0, a[n-a[n-1]] + a[n-a[n-2]]];
Array[a, 100] (* Paolo Xausa, May 31 2024 *)

cp's OEIS Frontend

A278066 Relative of Hofstadter Q-sequence: a(1) = 5, a(2) = 2; thereafter a(n) = a(n-a(n-1)) + a(n-a(n-2)).

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