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A087721 Strictly increasing domain of the Hofstadter batrachian sequence A005185. 0
2, 3, 4, 5, 6, 8, 10, 11, 12, 16, 20, 21, 22, 23, 24, 25, 30, 32, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 52, 54, 56, 58, 60, 61, 62, 64, 66, 68, 71, 72, 73, 77, 78, 79, 80, 82, 83, 85, 87, 88, 90, 91, 92, 93, 94, 96, 101, 106, 108, 109, 111, 114, 115, 118, 120, 122, 123 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This result came from discussion with Robert G. Wilson v about variations in chaotic sequences. The conclusion is that there are three distinct sets: (1) consecutive repeating, (2) strictly increasing and (3) strictly decreasing.

LINKS

Table of n, a(n) for n=1..68.

FORMULA

a(n) =a(n - a(n-1)) + a(n - a(n-2)).

MATHEMATICA

digits=750 Hofstadter[n_Integer?Positive] := Hofstadter[n] = Hofstadter[n - Hofstadter[n-1]] + Hofstadter[n - Hofstadter[n-2]] Hofstadter[1] = Hofstadter[2] = 1 a1=Table[Hofstadter[n], {n, 1, digits}]; f[x_, y_] := x-y/; x-y>0 f[x_, y_] := 0/; x-y<=0 b=Table[If[f[a1[[n]], a1[[n-1]]]>0, a1[[n]], 0], {n, 2, digits}]; c=Delete[Union[b], 1]

CROSSREFS

Cf. A005185, A087722, A087723.

Sequence in context: A291686 A057197 A067936 * A226244 A140642 A188936

Adjacent sequences:  A087718 A087719 A087720 * A087722 A087723 A087724

KEYWORD

nonn

AUTHOR

Roger L. Bagula, Sep 29 2003

STATUS

approved

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Last modified July 29 17:41 EDT 2021. Contains 346346 sequences. (Running on oeis4.)