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A133299 Fractal sequence of the Stolarsky array, A035506.

%I A133299 #27 May 18 2025 02:14:59
%S A133299 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,
%T A133299 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,
%U A133299 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
%N A133299 Fractal sequence of the Stolarsky array, A035506.
%D A133299 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
%H A133299 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/StolarskyArray.html">Stolarsky Array</a>
%F A133299 A035506(a(n),k)=n for some k>=1. - _R. J. Mathar_, Nov 21 2007
%F A133299 a(n) = 1+A098861(n). - _Casey Mongoven_, Sep 10 2011
%e A133299 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.
%p A133299 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:
%p A133299 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:
%p A133299 seq(A133299(n),n=1..100) ; # _R. J. Mathar_, Nov 21 2007
%t A133299 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]]]];
%t A133299 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[]]]]]];
%t A133299 Array[a, 100] (* _Jean-François Alcover_, Mar 22 2020, after _R. J. Mathar_ *)
%Y A133299 Cf. A035506, A098861, A195164.
%K A133299 nonn
%O A133299 1,4
%A A133299 _Gregg Whisler_, Oct 17 2007
%E A133299 Better definition from _R. J. Mathar_, Oct 22 2007
%E A133299 More terms from _R. J. Mathar_, Nov 21 2007
%E A133299 Definition now conforms to others; comment replaced - _Clark Kimberling_, Oct 29 2009