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A034589 Lucky numbers N (A000959) such that Fibonacci iterations starting with (1, N) lead to a "nine digits anagram".

%I A034589 #26 Feb 16 2025 08:32:37
%S A034589 8955,24405,30013,59325,62025,71493,72123,76885,85461,92077,99165,
%T A034589 106185,109717,112251,119077,148773,153007,155077,163771,163803,
%U A034589 196797,211369,221137,223365,227119,228271,228631
%N A034589 Lucky numbers N (A000959) such that Fibonacci iterations starting with (1, N) lead to a "nine digits anagram".
%C A034589 "Nine digits anagram" is a number whose digits are a permutation of {1, ..., 9}, also called restricted zeroless pandigital number. These are listed as the first 9! terms of A050289. - _M. F. Hasler_, Jan 10 2020
%H A034589 M. F. Hasler, <a href="/A034589/b034589.txt">Table of n, a(n) for n = 1..275</a> (using A000959(1..2e5) from b-file), Jan 10 2020
%H A034589 Patrick De Geest, <a href="http://www.worldofnumbers.com/ninedigits.htm">Nine Digits Digressions</a>
%H A034589 Eric Weisstein's World of Mathematics, <a href="https://mathworld.wolfram.com/LuckyNumber.html">Lucky Numbers</a>
%F A034589 Intersection of A000959 (lucky numbers) and A034587. - _M. F. Hasler_, Jan 10 2020
%e A034589 Denote by F(1, N) the Fibonacci sequence x(k+1) = x(k) + x(k-1) starting with x(0) = 1, x(1) = N.
%e A034589 Then for N = 228631, F(1, N) = (1, 228631, 228632, 457263, 685895, 1143158, 1829053, 2972211, 4801264, 7773475, 12574739, 20348214, 32922953, 53271167, 86194120, 139465287, ...), where a nine-digits anagram has been reached.
%o A034589 (PARI) A034589_upto(N)=[n|n<-A000959_upto(N),is_A034587(n)] \\ or select(is_A034587, A959=from("b000959.txt")). - _M. F. Hasler_, Jan 10 2020
%Y A034589 Cf. A000959 (lucky numbers), A050289 (zeroless pandigital numbers).
%Y A034589 Cf. A034587 (all starting values leading to 9-digit anagrams), A034588 (subset of primes), A034306 (subset of palindromes).
%K A034589 nonn,base,fini
%O A034589 1,1
%A A034589 _Patrick De Geest_, Oct 15 1998
%E A034589 Name, example & crossrefs edited, offset changed to 1 by _M. F. Hasler_, Jan 06 2020