

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
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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. BicknellJohnson, published by The Fibonacci Association, (1980) pp. 134136.  Casey Mongoven, Sep 10 2011


LINKS

Table of n, a(n) for n=1..85.
E. Weisstein, 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 c2 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


CROSSREFS

Cf. A195164.
Sequence in context: A194961 A195110 A167198 * A286537 A132163 A205682
Adjacent sequences: A133296 A133297 A133298 * A133300 A133301 A133302


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



