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

8955, 24405, 30013, 59325, 62025, 71493, 72123, 76885, 85461, 92077, 99165, 106185, 109717, 112251, 119077, 148773, 153007, 155077, 163771, 163803, 196797, 211369, 221137, 223365, 227119, 228271, 228631

Offset: 1

Author

Patrick De Geest, Oct 15 1998

Keywords

• nonn
• base
• fini

Comments

"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

Examples

			Denote by F(1, N) the Fibonacci sequence x(k+1) = x(k) + x(k-1) starting with x(0) = 1, x(1) = N.
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.
		

Links

• M. F. Hasler, Table of n, a(n) for n = 1..275 (using A000959(1..2e5) from b-file), Jan 10 2020
• Patrick De Geest, Nine Digits Digressions
• Eric Weisstein's World of Mathematics, Lucky Numbers

Crossrefs

Cf. A000959 (lucky numbers), A050289 (zeroless pandigital numbers).

Cf. A034587 (all starting values leading to 9-digit anagrams), A034588 (subset of primes), A034306 (subset of palindromes).

Programs

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

Formula

Intersection of A000959 (lucky numbers) and A034587. - M. F. Hasler, Jan 10 2020

Extensions

Name, example & crossrefs edited, offset changed to 1 by M. F. Hasler, Jan 06 2020