Least nonnegative number k such that Lucas(k) begins with the same digits as n.

1, 0, 2, 3, 13, 23, 4, 14, 19, 24, 5, 10, 15, 39, 20, 25, 49, 6, 11, 35, 59, 16, 64, 21, 45, 69, 26, 50, 7, 31, 55, 12, 36, 60, 17, 151, 41, 65, 22, 156, 46, 70, 27, 94, 51, 252, 8, 32, 166, 56, 190, 13, 281, 37, 305, 61, 18, 85, 42, 109, 310, 66, 267, 23, 224

1

Here Lucas(k) is the kth term of the sequence of Lucas numbers 2, 1, 3, 4, 7, 11, 18, 29, 47, 76, 123, 199, 322, 521,…. For example, the 13-th term of the Lucas sequence is the first to begin with 5. See the next sequence.

T. D. Noe, Plot of 10000 terms

T. D. Noe, Table of 10000 terms

Eric W. Weisstein, MathWorld: Lucas Number

(Mma) nn = 100; t = tn = Table[0, {nn}]; found = 0; n = -1; While[found < nn, n++; f = LucasL[n]; d = IntegerDigits[f]; i = 1; While[i <= Length[d], k = FromDigits[Take[d, i]]; If[k > nn, Break[]]; If[t[[k]] == 0, t[[k]] = f; tn[[k]] = n; found++]; i++]]; tn

Cf. A000032, A020344 (similar sequence for Fibonacci numbers), S000976.

nonn,base

T. D. Noe, Feb 28 2017