A087847 a(n) = a(|n - a(n-1)|) + a(a(a(|n - a(n-4)|))).

1, 1, 1, 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6, 7, 7, 7, 7, 7, 7, 7, 8, 8, 8, 8, 8, 8, 8, 8, 9, 9, 9, 9, 9, 9, 9, 9, 9, 10, 10, 10, 10, 10, 10, 10, 10, 10, 10, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 11, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 12, 13, 13, 13, 13, 13

Offset

1,5

Comments

The skip two term two fourth recursion of the Hofstadter Q.

The conjecture is that even higher order recursions of the term one and term two type for the original and skip term versions of A005185 Hofstadter Q will exist as well. I have invented this way of naming the larger generalization of Hofstadter Q type sequences as being descriptive of their formation.

From which numbers n>3 on is this sequence different from A002024(n-3), if ever? - M. F. Hasler, Apr 19 2014

Links

Table of n, a(n) for n=1..86.

Mathematica

Hofstadter14[n_Integer?Positive] := Hofstadter14[n] = Hofstadter14[Abs[n - Hofstadter14[n-1]]] + Hofstadter14[Hofstadter14[ Hofstadter14[Abs[n - Hofstadter14[n-4]]]]] Hofstadter14[0] = Hofstadter14[1] = Hofstadter14[2]= Hofstadter14[3]= Hofstadter14[4]= 1 digits=200 ta=Table[Hofstadter14[n], {n, 1, digits}]

Prog

(PARI) a(n) = if(n<5, return(1)); a(abs(n - a(n-1))) + a(a(a(abs(n - a(n-4))))) \\ Charles R Greathouse IV, Jan 20 2016

Crossrefs

Cf. A005185, A081831.

Sequence in context: A023965 A274094 A274093 * A107436 A002024 A123578

Adjacent sequences: A087844 A087845 A087846 * A087848 A087849 A087850

Keyword

nonn

Author

Roger L. Bagula, Oct 07 2003

Status

approved