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

1,1

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

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

Formula

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

Example

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.

Prog

(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

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).

Sequence in context: A172960 A172689 A172782 * A237164 A250368 A234755

Adjacent sequences: A034586 A034587 A034588 * A034590 A034591 A034592

Keyword

nonn,base,fini

Author

Patrick De Geest, Oct 15 1998

Extensions

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

Status

approved