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A026274 Greatest k such that s(k) = n, where s = A026272. 10
3, 5, 8, 11, 13, 16, 18, 21, 24, 26, 29, 32, 34, 37, 39, 42, 45, 47, 50, 52, 55, 58, 60, 63, 66, 68, 71, 73, 76, 79, 81, 84, 87, 89, 92, 94, 97, 100, 102, 105, 107, 110, 113, 115, 118, 121, 123, 126, 128, 131, 134, 136, 139, 141, 144 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

This is the upper s-Wythoff sequence, where s(n)=n+1.

See comments at A026273.

Conjecture: This sequence consists precisely of those numbers without a 1 or 2 in their Zeckendorf representation. [In other words, numbers which are the sum of distinct Fibonacci numbers greater than 2.] - Charles R Greathouse IV, Jan 28 2015

A Beatty sequence with complement A026273. - Robert G. Wilson v, Jan 30 2015

A035612(a(n)+1) = 1. - Reinhard Zumkeller, Jul 20 2015

From Michel Dekking, Mar 12 2018: (Start)

One has r*r*(n-2*r+3) = n*r^2 -2r^3+3*r^2 = (n+1)*r^2 -2, where r = (1+sqrt(5))/2.

So  a(n) = (n+1)*r^2-2, and we see that this sequence is simply the Beatty sequence of the square of the golden ratio, shifted spatially and temporally. In other words if w = A001950 = 2,5,7,10,13,15,18,20,...  is the upper Wythoff sequence, then a(n)=w(n+1)-2.

(End)

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

FORMULA

a(n) = floor(r*r*(n+2r-3)), where r = (1+sqrt(5))/2 = A001622. [Corrected by Tom Edgar, Jan 30 2015]

a(n) = 3*n - floor[(n+1)/(1+phi)], phi = (1+sqrt(5))/2. - Joshua Tobin (tobinrj(AT)tcd.ie), May 31 2008

MATHEMATICA

r=(1+Sqrt[5])/2;

a[n_]:=Floor[r*r*(n+2r-3)];

Table[a[n], {n, 200}]

PROG

(Haskell)

a026274 n = a026274_list !! (n-1)

a026274_list = map (subtract 1) $ tail $ filter ((== 1) . a035612) [1..]

-- Reinhard Zumkeller, Jul 20 2015

CROSSREFS

Cf. A184117, A026273, A001950.

Sequence in context: A213732 A247909 A184659 * A137910 A022850 A008576

Adjacent sequences:  A026271 A026272 A026273 * A026275 A026276 A026277

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

Extended by Clark Kimberling, Jan 14 2011

STATUS

approved

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Last modified August 21 21:42 EDT 2018. Contains 313957 sequences. (Running on oeis4.)