A130792 Numbers k whose representation can be split in two parts which can be used as seeds for a Fibonacci-like sequence containing k itself.

14, 19, 28, 47, 61, 75, 122, 149, 183, 199, 244, 298, 305, 323, 366, 427, 488, 497, 549, 646, 795, 911, 969, 1292, 1301, 1499, 1822, 1999, 2087, 2602, 2733, 2998, 3089, 3248, 3379, 3644, 3903, 4555, 4997, 5204, 5466, 6178, 6377, 6496, 6505, 7288, 7806, 7995

Offset

1,1

Comments

The 6 terms with two digits are also Keith numbers. There are 233 numbers below 10^6 in this sequence.

Links

Michel Marcus, Table of n, a(n) for n = 1..406 (first 200 terms from Paolo Lava)

Example

122 can be split into 12 and 2 and the Fibonacci-like sequence: 12, 2, 14, 16, 30, 46, 76, 122, ... contains 122 itself.

Mathematica

testQ[n_]:= Block[{x, y, z, p = 10, r = False}, While[p < n, x = Floor[n/p]; y = Mod[n, p]; While[y < n, z = x + y; x = y; y = z]; If[y == n, r = True; Break[]]; p *= 10]; r]; Select[Range[10^4], testQ]

Prog

(PARI) isok(n) = {nb = #Str(n); for (i=1, nb-1, x = n\10^i; y = n - 10^i*x; ok = 0; while(!ok, z = x + y; if (z > n, ok = 1); if (z == n, return (1)); x = y; y = z; )); } \\ Michel Marcus, Oct 08 2014

Crossrefs

Cf. A007629.

Sequence in context: A120158 A292614 A305484 * A121235 A007629 A349421

Adjacent sequences: A130789 A130790 A130791 * A130793 A130794 A130795

Keyword

base,nonn

Author

Giovanni Resta, Aug 20 2007

Status

approved