login
A355439
Smallest Lucas number beginning with n.
2
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
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
KEYWORD
nonn,base
AUTHOR
Michel Marcus, Jul 02 2022
STATUS
approved