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A133299
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Fractal sequence of the Stolarsky array, A035506.
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40
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1, 1, 1, 2, 1, 2, 3, 1, 4, 2, 3, 5, 1, 6, 4, 2, 7, 3, 5, 8, 1, 9, 6, 4, 10, 2, 11, 7, 3, 12, 5, 8, 13, 1, 14, 9, 6, 15, 4, 10, 16, 2, 17, 11, 7, 18, 3, 19, 12, 5, 20, 8, 13, 21, 1, 22, 14, 9, 23, 6, 15, 24, 4, 25, 10, 16, 26, 2, 27, 17, 11, 28, 7, 18, 29, 3, 30, 19, 12, 31, 5, 32, 20, 8, 33
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OFFSET
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1,4
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REFERENCES
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D. R. Morrison, A Stolarsky Array of Wythoff Pairs, A Collection of Manuscripts Related to the Fibonacci Sequence, edited by V. E. Hoggatt Jr., M. Bicknell-Johnson, published by The Fibonacci Association, (1980) pp. 134-136. - Casey Mongoven, Sep 10 2011
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LINKS
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FORMULA
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EXAMPLE
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As a fractal sequence, if each first occurrence of each n is deleted, then the resulting sequence is the same as the original. For the fractal sequence of the Wythoff array, see A003603.
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MAPLE
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A035506 := proc(r, c) local tau, a, b, d, i ; tau := (1+sqrt(5))/2 ; a := floor( r*(1+tau)-tau/2) ; b := round(a*tau) ; if c = 1 then RETURN(a) ; else if c =2 then RETURN(b) ; else for i from 1 to c-2 do d := a+b ; a := b; b := d ; od: RETURN(d) ; fi ; fi ; end:
A133299 := proc(n) local row, col ; for row from 1 do for col from 1 do stola := A035506(row, col) ; if stola = n then RETURN(row) ; elif stola > n then break ; fi ; od: od: end:
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MATHEMATICA
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A035506[r_, c_] := Module[{tau = GoldenRatio, a, b, d, i}, a = Floor[r*(1 + tau) - tau/2]; b = Round[a*tau]; If[c == 1, Return[a], If[c == 2, Return[b], For[i = 1, i <= c - 2, i++, d = a + b; a = b; b = d]; Return[d]]]];
a[n_] := Module[{row, col}, For[row = 1, True, row++, For[col = 1, True, col++, stola = A035506[row, col] ; If[stola == n, Return[row], If[stola > n, Break[]]]]]];
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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Definition now conforms to others; comment replaced - Clark Kimberling, Oct 29 2009
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STATUS
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approved
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