A112516 -id:A112516 - cp's OEIS frontend

A112371 Numbers n such that the last 9 decimal digits of the n-th Fibonacci number is pandigital 1-9.

541, 919, 1788, 6355, 16257, 17799, 20411, 24347, 28837, 36485, 40784, 43450, 45136, 45196, 51973, 54453, 54833, 57128, 57969, 63692, 67188, 67952, 69931, 74765, 76259, 78102, 78196, 78826, 81070, 81726, 87123, 87362, 91636, 91932

Offset: 1

Roger Hui, Dec 22 2005

Since the Fibonacci sequence mod 10^9 is periodic with period 1500000000, there is some positive M such that this sequence satisfies a(n+M) = a(n) + 1500000000. - Robert Israel, Jan 18 2015

			The 541st Fibonacci number is:
51621 23292 73937 94428 28328 17223 02417 68441 62155 65352
08137 22196 49050 89439 99028 11978 84249 30258 98332 77779
69788 39725 641
which is pandigital 1-9 in its last 9 digits.

Clifford A. Pickover, "Wonders of Numbers".

Norman Morton and Michael Satteson, Table of n, a(n) for n = 1..10000, (first 150 terms from Norman Morton)

Cf. A000045, A112516.

NB. In J (www.jsoftware.com).
f=: 3 : '{."(1) 1e9&|@(+/\)@|.^:( ":&.> f n

f:= proc(n) option remember; f(n-1)+f(n-2) mod 10^9 end proc:
f(0):= 0: f(1):= 1:
filter:= n -> convert(convert(f(n),base,10),set)={$1..9};
select(filter, [$1..10^5]); # Robert Israel, Jan 18 2015

A112512 Say what you see in previous term, same as A063850, but starting with 2.

Original entry on oeis.org

2, 12, 1112, 3112, 132112, 311322, 232122, 421311, 14123113, 41141223, 24312213, 32142321, 23322114, 32232114, 23322114, 32232114, 23322114, 32232114

Offset: 1

Michele Dondi (blazar(AT)lcm.mi.infn.it), Sep 09 2005

Eventually periodic, eventually identical (to a shift of) A063850.

Cf. A005150, A005151, A063850, A112512-A112516.

#!/usr/bin/perl -l use strict; use warnings; die "Usage: $0  " unless @ARGV==1; $=shift; { print; my (%cnt, %saw); $cnt{$}++ for /./g; s/./ $saw{$&}++ ? '' : $cnt{$&} . $& /ge; <>, redo; } _END_

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

Original entry on oeis.org

3352, 3837, 7239, 18503, 19344, 22628, 29363, 30994, 37514, 47058, 48201, 50371, 51702, 51857, 53586, 55469, 56248, 56668, 60560, 65206, 70610, 72171, 76554, 78310, 78380, 82628, 82952, 82993, 93615, 99751, 101179, 104469, 105347, 105379, 106327, 113251, 114970, 116751, 117313

Offset: 1

V. Raman, Sep 07 2012

V. Raman, Table of n, a(n) for n = 1..10000
Project Euler, Problem 104: Pandigital Fibonacci ends.

Cf. A000032.
Cf. A112516 for Fibonacci numbers such that first 9 digits are 1-9 pandigital.
Cf. A112371 for Fibonacci numbers such that last 9 digits are 1-9 pandigital.

b:= proc(n) b(n):= `if`(n<2, 2-n, irem(b(n-1)+b(n-2), 10^9)) end:
q:= n-> is({convert(b(n), base, 10)[]}={$1..9}):
select(q, [$1..120000])[];  # Alois P. Heinz, Jul 04 2021

Select[Range[39, 120000], Sort[Take[IntegerDigits[LucasL[#]], -9]] == {1, 2, 3, 4, 5, 6, 7, 8, 9} &] (* Tanya Khovanova, Jul 04 2021 *)

def afind(limit):
    bkm1, bk = 2, 1
    for k in range(2, limit+1):
        bkm1, bk = bk, bkm1 + bk
        if set(str(bk)[-9:]) == set("123456789"): print(k, end=", ")
afind(10**6) # Michael S. Branicky, Jul 04 2021

A216489 Numbers k such that the first 9 digits of the k-th Lucas number are 1-9 pandigital.

Original entry on oeis.org

10524, 10960, 11199, 15957, 16247, 17734, 20187, 29879, 30046, 31998, 38874, 40181, 44757, 47078, 47773, 48101, 49125, 50674, 50717, 51607, 54399, 57943, 59563, 64305, 64453, 68160, 76227, 77624, 84268, 86070, 89792, 91069, 91496, 92481, 95472, 97418, 97698, 98390, 99021

Offset: 1

V. Raman, Sep 07 2012

V. Raman, Table of n, a(n) for n = 1..10000
Project Euler, Problem 104: Pandigital Fibonacci ends.

Cf. A112516 for Fibonacci numbers such that first 9 digits are 1-9 pandigital.

Cf. A112371 for Fibonacci numbers such that last 9 digits are 1-9 pandigital.

cp's OEIS Frontend

A112371 Numbers n such that the last 9 decimal digits of the n-th Fibonacci number is pandigital 1-9.

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A112512 Say what you see in previous term, same as A063850, but starting with 2.

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

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A216489 Numbers k such that the first 9 digits of the k-th Lucas number are 1-9 pandigital.

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