A355439 Smallest Lucas number beginning with n.

1, 2, 3, 4, 521, 64079, 7, 843, 9349, 103682, 11, 123, 1364, 141422324, 15127, 167761, 17393796001, 18, 199, 20633239, 2139295485799, 2207, 23725150497407, 24476, 2537720636, 263115950957276, 271443, 28143753123, 29, 3010349, 312119004989, 322, 33385282, 3461452808002, 3571

Offset: 1

Author

Michel Marcus, Jul 02 2022

Keywords

• nonn
• base

Comments

a(1382) is the first term with > 1000 digits (1156). - Michael S. Branicky, Jul 08 2022

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..1381
• Ron Knott, Every number starts some Fibonacci Number, The Mathematical Magic of the Fibonacci Numbers.

Crossrefs

Cf. A000032, A355438.

Cf. A020344, A020345.

Programs

PARI

L(n) = real((2 + quadgen(5)) * quadgen(5)^n); \\ A000032
isok(k, dn) = my(dk=digits(L(k))); if (#dk >= #dn, Vec(dk, #dn) == dn);
a(n) = my(k=0, dn=digits(n)); while (!isok(k, dn), k++); L(k);

Python

def aupton(nn):
    ans, f, g, k = dict(), 2, 1, 0
    while len(ans) < nn:
        sf = str(f)
        for i in range(1, len(sf)+1):
            if int(sf[:i]) > nn:
                break
            if sf[:i] not in ans:
                ans[sf[:i]] = f
        f, g, k = g, f+g, k+1
    return [int(ans[str(i)]) for i in range(1, nn+1)]
print(aupton(35)) # Michael S. Branicky, Jul 08 2022