A034306 Palindromes P such that Fibonacci iterations starting with (1, P) lead to a "nine digits anagram".

4004, 630036, 1559551, 4187814, 4870784, 6097906, 6834386, 9530359, 50755705, 51733715, 54988945, 62399326, 62488426, 63299236, 63477436, 64288246, 64377346, 71399317, 71488417, 73199137, 73466437, 74188147, 74366347, 81299218, 81477418, 82199128, 82466428, 84177148, 84266248

Offset: 1

Author

Patrick De Geest, Oct 15 1998

Keywords

• nonn
• base
• fini
• full

Comments

A "nine digit anagram" is a (so-called restricted zeroless pandigital) number whose digits are a permutation of [1..9], i.e., one of the first 9! terms of A050289.

In total there are exactly 68 such palindromes, 437606734 is the largest.

Examples

			Denote by F(1,P) the Fibonacci type sequence x(n+1) = x(n) + x(n-1) with x(0) = 1, x(1) = P.
Then for P = a(8) = 9530359, F(1,P) = (1, 9530359, 9530360, 19060719, 28591079, 47651798, 76242877, 123894675, ...) where a 9-digits anagram has occurred.
		

Links

• Giovanni Resta, Table of n, a(n) for n = 1..68 (full sequence)
• Patrick De Geest, Nine Digits Digressions

Crossrefs

Cf. A002113 (palindromes), A050289 (zeroless pandigital numbers).

Cf. A034587 (all starting values leading to 9-digit anagrams), A034588 (subset of primes), A034589 (subset of lucky numbers).

Programs

PARI

A034306=[p | p<-[A002113(n) | n<-[1..6*10^4]], is_A034587(p)] \\ All 68 terms in a fraction of a second. - M. F. Hasler, Jan 08 2020

Formula

Intersection of A034587 and A002113 (palindromes). - M. F. Hasler, Jan 08 2020

Extensions

Edited by M. F. Hasler, Jan 09 2020