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A360259
a(0) = 0, and for any n > 0, let k > 0 be as small as possible and such that F(2) + ... + F(1+k) >= n (where F(m) denotes A000045(m), the m-th Fibonacci number); a(n) = k + a(F(2) + ... + F(1+k) - n).
3
0, 1, 3, 2, 6, 4, 3, 10, 6, 7, 5, 4, 15, 8, 9, 11, 7, 8, 6, 5, 21, 10, 11, 13, 12, 16, 9, 10, 12, 8, 9, 7, 6, 28, 12, 13, 15, 14, 18, 16, 15, 22, 11, 12, 14, 13, 17, 10, 11, 13, 9, 10, 8, 7, 36, 14, 15, 17, 16, 20, 18, 17, 24, 20, 21, 19, 18, 29, 13, 14, 16
OFFSET
0,3
COMMENTS
See A095791 for the corresponding k's.
This sequence has similarities with A227192; here we use Fibonacci numbers, there powers of 2.
LINKS
FORMULA
a(A001911(n)) = n.
EXAMPLE
The first terms, alongside the corresponding k's, are:
n a(n) k
----- ---- ---
0 0 N/A
1 1 1
2 3 2
3 2 2
4 6 3
5 4 3
6 3 3
7 10 4
8 6 4
9 7 4
10 5 4
11 4 4
12 15 5
PROG
(PARI) { t = k = 0; print1 (0); for (n = 1, #a = vector(70), if (n > t, t += fibonacci(1+k++); ); print1 (", "a[n] = k+if (t==n, 0, a[t-n])); ); }
CROSSREFS
See A095791, A360260 and A360265 for similar sequences.
Sequence in context: A121647 A339333 A339334 * A340873 A033940 A286367
KEYWORD
nonn,look
AUTHOR
Rémy Sigrist, Jan 31 2023
STATUS
approved