

A284282


a(n) = the number k such that A030067(2k1) = n, or 0 if n does not occur in the semiFibonacci 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
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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 oddindexed term A030067(2k1) = A030068(k1), and thereafter at indices (2k1)*2^j, j=1,2,3,... (Both of these statements follow immediately from the definition of evenindexed terms of A030067.)
It is easy to see that no n can occur a second time as an oddindexed term in A030067. This follows from the definition of these terms A030067(2k+1) = A030067(2k1) + A030067(k), which shows that the subsequence of oddindexed terms (A030068) is strictly increasing, and therefore equal to the range (or: set) of all semiFibonacci 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 JeanFrançois 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 (semiFibonacci sequence), A030068 (bisection of oddindexed terms, also equal to the range = set of all possible values or semiFibonacci 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



