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Least number k such that the Lucas number A000032(k) contains n.
1

%I #12 Jun 07 2017 00:35:09

%S 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,

%T 20,36,7,31,50,12,35,19,17,15,41,36,22,23,39,39,14,21,41,60,8,32,19,

%U 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

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

%C 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]

%H Chai Wah Wu, <a href="/A132365/b132365.txt">Table of n, a(n) for n = 1..10000</a>

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

%o (Python)

%o def A132365(n):

%o a, b, m, s = 2, 1, 0, str(n)

%o while True:

%o if s in str(a):

%o return m

%o m += 1

%o a, b = b, a+b # _Chai Wah Wu_, Jun 06 2017

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

%K base,easy,nonn

%O 1,3

%A _Jonathan Vos Post_, Nov 08 2007

%E Incorrect comment removed by _Sean A. Irvine_, Nov 30 2009

%E Corrected and extended by _Sean A. Irvine_, Nov 30 2009