A325171 Down-integers: integers k such that w_(s+1) = floor(phi*k) for some k-slow Fibonacci walk, with phi=(1+sqrt(5))/2. See comments for further explanation.
2, 5, 7, 9, 10, 12, 13, 15, 18, 23, 26, 28, 31, 33, 34, 36, 38, 39, 41, 43, 44, 46, 47, 48, 49, 51, 52, 54, 56, 57, 59, 60, 62, 64, 65, 67, 68, 70, 72, 73, 75, 78, 80, 81, 83, 86, 88, 89, 91, 94, 96, 99, 102, 104, 107, 112, 115, 120, 123, 125, 128, 133, 136, 138, 141, 146, 149
Offset: 1
Keywords
Links
- Fan Chung, Ron Graham, and Sam Spiro, Slow Fibonacci Walks, arXiv:1903.08274 [math.NT], 2019. See pp. 3-4.
Programs
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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 isdown(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 == floor(n*((1+sqrt(5))/2)), return (1));););); return (0);}
Comments