

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
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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(n1)) + a(n  a(n2)).


MATHEMATICA

digits=750 Hofstadter[n_Integer?Positive] := Hofstadter[n] = Hofstadter[n  Hofstadter[n1]] + Hofstadter[n  Hofstadter[n2]] Hofstadter[1] = Hofstadter[2] = 1 a1=Table[Hofstadter[n], {n, 1, digits}]; f[x_, y_] := xy/; xy>0 f[x_, y_] := 0/; xy<=0 b=Table[If[f[a1[[n]], a1[[n1]]]>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



