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A284282 a(n) = the number k such that A030067(2k-1) = n, or 0 if n does not occur in the semi-Fibonacci sequence A030067. 2
0, 1, 2, 3, 0, 4, 5, 0, 0, 6, 0, 7, 0, 0, 0, 0, 8, 9, 0, 0, 0, 0, 0, 10, 0, 0, 11, 0, 0, 0, 0, 0, 0, 0, 0, 12, 0, 13, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 14, 0, 0, 0, 0, 15, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 16, 17, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 18 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Otherwise said, a(n) = round(m/2) = (m+1)/2, where m is the smallest index such that A030067(m) = n.

Any integer n which occurs in A030067 first occurs as an odd-indexed term A030067(2k-1) = A030068(k-1), and thereafter at indices (2k-1)*2^j, j=1,2,3,... (Both of these statements follow immediately from the definition of even-indexed terms of A030067.)

It is easy to see that no n can occur a second time as an odd-indexed term in A030067. This follows from the definition of these terms A030067(2k+1) = A030067(2k-1) + A030067(k), which shows that the subsequence of odd-indexed terms (A030068) is strictly increasing, and therefore equal to the range (or: set) of all semi-Fibonacci numbers.

Setting all nonzero terms to 1, this sequence is the characteristic function of A030068 (up to the offset).

LINKS

Table of n, a(n) for n=0..87.

MATHEMATICA

a[n_] := a[n] = Which[n == 1, 1, EvenQ@ n, a[n/2], True, a[n - 1] + a[n - 2]]; With[{nn = 87}, Function[s, Function[t, {0}~Join~ReplacePart[t, Map[# -> First@ Lookup[s, #] &, TakeWhile[Keys@ s, # <= nn &]]]]@ ConstantArray[0, nn]]@ PositionIndex@ Array[a[2 # - 1] &, 10^3]] (* Michael De Vlieger, Mar 25 2017, Version 10, after Jean-François Alcover at A030067 *)

PROG

(PARI) A284282(n)=setsearch(A030068_vec, n) \\ Use, e.g., A030068(100) to compute the global variable A030068_vec far enough for n <= 22880. - M. F. Hasler, Mar 25 2017

CROSSREFS

Cf. A030067 (semi-Fibonacci sequence), A030068 (bisection of odd-indexed terms, also equal to the range = set of all possible values or semi-Fibonacci numbers).

Sequence in context: A140502 A175434 A154860 * A132774 A294721 A300816

Adjacent sequences:  A284279 A284280 A284281 * A284283 A284284 A284285

KEYWORD

nonn

AUTHOR

M. F. Hasler, Mar 24 2017

STATUS

approved

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Last modified September 29 14:20 EDT 2022. Contains 357090 sequences. (Running on oeis4.)