A132365 Least number k such that the Lucas number A000032(k) contains n.

1, 0, 2, 3, 13, 9, 4, 6, 7, 24, 5, 10, 15, 26, 20, 25, 49, 6, 11, 16, 13, 12, 10, 21, 45, 40, 20, 36, 7, 31, 50, 12, 35, 19, 17, 15, 41, 36, 22, 23, 39, 39, 14, 21, 41, 60, 8, 32, 19, 56, 20, 13, 45, 37, 51, 44, 17, 56, 42, 22, 25, 62, 35, 15, 71, 47, 25, 24, 43, 32, 17, 45, 49, 38

Offset

1,3

Comments

Values such that a(n)=n (fixed points) are 1, 62. I don't know if there are any other fixed points. The first time a(n)=a(n+1) occurs because L(39)=141422324 which includes both 41 and 42 (and later on in the sequence, because it contains 141 and 142). [Sean A. Irvine, Nov 30 2009]

Links

Chai Wah Wu, Table of n, a(n) for n = 1..10000

Formula

a(n) = Min{k such that A000032(k) contains the decimal digit substring which represents the integer n}.

Prog

(Python)
def A132365(n):
    a, b, m, s = 2, 1, 0, str(n)
    while True:
        if s in str(a):
            return m
        m += 1
        a, b = b, a+b # Chai Wah Wu, Jun 06 2017

Crossrefs

Cf. A000032, A000045, A000350, A050816, A038546, A052000, A023172.

Sequence in context: A110362 A074478 A046421 * A129671 A117684 A056445

Adjacent sequences: A132362 A132363 A132364 * A132366 A132367 A132368

Keyword

base,easy,nonn

Author

Jonathan Vos Post, Nov 08 2007

Extensions

Incorrect comment removed by Sean A. Irvine, Nov 30 2009

Corrected and extended by Sean A. Irvine, Nov 30 2009

Status

approved