login
A034306
Palindromes P such that Fibonacci iterations starting with (1, P) lead to a "nine digits anagram".
4
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
1,1
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.
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..68 (full sequence)
Patrick De Geest, Nine Digits Digressions
FORMULA
Intersection of A034587 and A002113 (palindromes). - M. F. Hasler, Jan 08 2020
EXAMPLE
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.
PROG
(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
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).
Sequence in context: A061700 A218641 A092722 * A228579 A252328 A235307
KEYWORD
nonn,base,fini,full
AUTHOR
Patrick De Geest, Oct 15 1998
EXTENSIONS
Edited by M. F. Hasler, Jan 09 2020
STATUS
approved