VOOZH about

URL: https://oeis.org/A325172

⇱ A325172 - OEIS

login
A325172
Up-integers: integers k such that w_(s+1) = ceiling(phi*k) for some k-slow Fibonacci walk, with phi=(1+sqrt(5))/2. See comments for further explanation.
1
3, 4, 6, 8, 11, 14, 16, 17, 19, 20, 21, 22, 24, 25, 27, 29, 30, 32, 35, 37, 40, 42, 45, 50, 53, 55, 58, 61, 63, 66, 69, 71, 74, 76, 77, 79, 82, 84, 85, 87, 90, 92, 93, 95, 97, 98, 100, 101, 103, 105, 106, 108, 109, 110, 111, 113, 114, 116, 117, 118, 119, 121, 122, 124
OFFSET
1,1
COMMENTS
An n-slow Fibonacci walk is a Fibonacci-like sequence that needs a maximum number of steps, s (see A088527), to reach n, and w_(s+1) will be the next term of this sequence. See Chung et al. for further explanation.
LINKS
Fan Chung, Ron Graham, and Sam Spiro, Slow Fibonacci Walks, arXiv:1903.08274 [math.NT], 2019. See pp. 3-4.
PROG
(PARI) nbs(i, j, n) = {my(nb = 2, ij); until (j >= n, ij = i+j; i = j; j = ij; nb++); if (j==n, nb, -oo); }
dofib(i, j, nb) = {if (nb==2, return (j)); for (k=3, nb, ij = i + j; i = j; j = ij; ); return (j); }
s(n) = {my(nb = 2, k); for (i=1, n, for (j=1, n, k = nbs(i, j, n); if (k> nb, nb = k); ); ); nb; } \\ A088527
isup(n) = {my(nb = s(n)); for (i=1, n, for (j=1, n, k = nbs(i, j, n); if (k == nb, w = dofib(i, j, nb+1); if (w == ceil(n*((1+sqrt(5))/2)), return (1)); ); ); ); return (0); }
CROSSREFS
Cf. A001622 (phi), A088527, A325171.
Sequence in context: A079401 A156040 A377979 * A365271 A390086 A242254
KEYWORD
nonn
AUTHOR
Michel Marcus, Apr 04 2019
STATUS
approved