A133299 Fractal sequence of the Stolarsky array, A035506.

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

Offset: 1

Author

Gregg Whisler, Oct 17 2007

Keywords

• nonn

Examples

			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.
		

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

Crossrefs

Cf. A035506, A098861, A195164.

Programs

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 *)

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

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