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 A319952 Let M = A022342(n) be the n-th number whose Zeckendorf representation is even; then a(n) = A129761(M). 1
 1, 2, 3, 1, 6, 1, 2, 11, 1, 2, 3, 1, 22, 1, 2, 3, 1, 6, 1, 2, 43, 1, 2, 3, 1, 6, 1, 2, 11, 1, 2, 3, 1, 86, 1, 2, 3, 1, 6, 1, 2, 11, 1, 2, 3, 1, 22, 1, 2, 3, 1, 6, 1, 2, 171, 1, 2, 3, 1, 6, 1, 2, 11, 1, 2, 3, 1, 22, 1, 2, 3, 1, 6, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 2,2 COMMENTS The Zeckendorf representations of numbers are given in A014417. The even ones are specified by A022342. The offset here is 2 (because A129761 should really have had offset 1 not 0). LINKS Table of n, a(n) for n=2..75. FORMULA If the Zeckendorf representation of M ends with exactly k zeros, ...10^k, then a(n) = ceiling(2^k/3). MAPLE with(combinat): F:=fibonacci: A130234 := proc(n) local i; for i from 0 do if F(i) >= n then return i; end if; end do: end proc: A014417 := proc(n) local nshi, Z, i ; if n <= 1 then return n; end if; nshi := n ; Z := [] ; for i from A130234(n) to 2 by -1 do if nshi >= F(i) and nshi > 0 then Z := [1, op(Z)] ; nshi := nshi-F(i) ; else Z := [0, op(Z)] ; end if; end do: add( op(i, Z)*10^(i-1), i=1..nops(Z)) ; end proc: A072649:= proc(n) local j; global F; for j from ilog[(1+sqrt(5))/2](n) while F(j+1)<=n do od; (j-1); end proc: A003714 := proc(n) global F; option remember; if(n < 3) then RETURN(n); else RETURN((2^(A072649(n)-1))+A003714(n-F(1+A072649(n)))); fi; end proc: A129761 := n -> A003714(n+1)-A003714(n): a:=[]; for n from 1 to 120 do if (A014417(n) mod 2) = 0 then a:=[op(a), A129761(n-1)]; fi; od; a; CROSSREFS Cf. A003714, A014417, A022342, A072649, A129761, A130234. Sequence in context: A137211 A212275 A189036 * A174665 A256470 A318198 Adjacent sequences: A319949 A319950 A319951 * A319953 A319954 A319955 KEYWORD nonn AUTHOR Jeffrey Shallit and N. J. A. Sloane, Oct 03 2018 STATUS approved

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Last modified December 3 02:05 EST 2023. Contains 367530 sequences. (Running on oeis4.)