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.

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

Table of n, a(n) for n=1..64.

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: A060903 A079401 A156040 * A365271 A242254 A107770

Adjacent sequences: A325169 A325170 A325171 * A325173 A325174 A325175

Keyword

nonn

Author

Michel Marcus, Apr 04 2019

Status

approved