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A133299 Fractal sequence of the Stolarsky array, A035506. 40
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 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,4
REFERENCES
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
LINKS
Eric Weisstein's World of Mathematics, Stolarsky Array
FORMULA
A035506(a(n),k)=n for some k>=1. - R. J. Mathar, Nov 21 2007
a(n) = 1+A098861(n). - Casey Mongoven, Sep 10 2011
EXAMPLE
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.
MAPLE
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:
seq(A133299(n), n=1..100) ; # R. J. Mathar, Nov 21 2007
MATHEMATICA
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[]]]]]];
Array[a, 100] (* Jean-François Alcover, Mar 22 2020, after R. J. Mathar *)
CROSSREFS
Sequence in context: A195110 A167198 A295540 * A286537 A132163 A355079
KEYWORD
nonn
AUTHOR
Gregg Whisler, Oct 17 2007
EXTENSIONS
Better definition from R. J. Mathar, Oct 22 2007
More terms from R. J. Mathar, Nov 21 2007
Definition now conforms to others; comment replaced - Clark Kimberling, Oct 29 2009
STATUS
approved

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Last modified March 19 03:33 EDT 2024. Contains 370952 sequences. (Running on oeis4.)