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A216488 Numbers k such that the last 9 digits of the k-th Lucas number are 1-9 pandigital.

%I A216488 #24 Mar 18 2023 12:38:30
%S A216488 3352,3837,7239,18503,19344,22628,29363,30994,37514,47058,48201,50371,
%T A216488 51702,51857,53586,55469,56248,56668,60560,65206,70610,72171,76554,
%U A216488 78310,78380,82628,82952,82993,93615,99751,101179,104469,105347,105379,106327,113251,114970,116751,117313
%N A216488 Numbers k such that the last 9 digits of the k-th Lucas number are 1-9 pandigital.
%H A216488 V. Raman, <a href="/A216488/b216488.txt">Table of n, a(n) for n = 1..10000</a>
%H A216488 Project Euler, <a href="https://projecteuler.net/problem=104">Problem 104: Pandigital Fibonacci ends</a>.
%p A216488 b:= proc(n) b(n):= `if`(n<2, 2-n, irem(b(n-1)+b(n-2), 10^9)) end:
%p A216488 q:= n-> is({convert(b(n), base, 10)[]}={$1..9}):
%p A216488 select(q, [$1..120000])[];  # _Alois P. Heinz_, Jul 04 2021
%t A216488 Select[Range[39, 120000], Sort[Take[IntegerDigits[LucasL[#]], -9]] == {1, 2, 3, 4, 5, 6, 7, 8, 9} &] (* _Tanya Khovanova_, Jul 04 2021 *)
%o A216488 (Python)
%o A216488 def afind(limit):
%o A216488     bkm1, bk = 2, 1
%o A216488     for k in range(2, limit+1):
%o A216488         bkm1, bk = bk, bkm1 + bk
%o A216488         if set(str(bk)[-9:]) == set("123456789"): print(k, end=", ")
%o A216488 afind(10**6) # _Michael S. Branicky_, Jul 04 2021
%Y A216488 Cf. A000032.
%Y A216488 Cf. A112516 for Fibonacci numbers such that first 9 digits are 1-9 pandigital.
%Y A216488 Cf. A112371 for Fibonacci numbers such that last 9 digits are 1-9 pandigital.
%K A216488 nonn,base
%O A216488 1,1
%A A216488 _V. Raman_, Sep 07 2012