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

1,2

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.

Prog

(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

Crossrefs

Cf. A000032, A355438.

Cf. A020344, A020345.

Sequence in context: A116022 A172998 A004888 * A062928 A004899 A085081

Adjacent sequences: A355436 A355437 A355438 * A355440 A355441 A355442

Keyword

nonn,base

Author

Michel Marcus, Jul 02 2022

Status

approved