A034587 -id:A034587 - cp's OEIS frontend

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

Patrick De Geest, Oct 15 1998

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.

			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.

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

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).

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

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

Edited by M. F. Hasler, Jan 09 2020

A034588 Primes p such that the Fibonacci iterations starting with (1, p) lead to a "nine digits anagram".

Original entry on oeis.org

1993, 8039, 22303, 30013, 31727, 46559, 50207, 63617, 65437, 72617, 83813, 92077, 101869, 102013, 109717, 131479, 136897, 141413, 145283, 156139, 162257, 163771, 204487, 206951, 207301, 209669, 211369, 221587, 221719, 225133, 225349, 233419

Offset: 1

Patrick De Geest, Oct 15 1998

A "nine digits anagram" is a number whose digits are a permutation of {1, ..., 9}, or one of the first 9! terms of A050289.
Largest term is a(46494) = 987653411.
Subset of primes in A034587. There are 767 (resp. 2982, resp. 6045) primes among the first 10^4 (resp. 5*10^4, resp. 10^5) terms of A034587, and (0, 1, 14, 129, 1566) terms among the first (100, 10^3, 10^4, 10^5, 10^6) primes, the last of which is 15480869 = prime(999708).  - M. F. Hasler, Jan 06 2020
The terms larger than 987654320/2 = 493827160 are primes of the form A050289(k)-1 with 158324 <= k <= 9!, cf. A034587. There are exactly 13005 of these which are therefore the last 13005 terms of this sequence, starting with 493851671 = A050289(158332)-1 = prime(26048750). - M. F. Hasler, Jan 09 2020
The graph of this sequence has a distinct slope for values below, between, and above the two limits of 2.07e8 and 4.94e8, as for the graph of A034587 (cf. link). - M. F. Hasler, Jan 11 2020

			Starting with (1, 233419), Fibonacci iterations x(n+1) = x(n) + x(n-1) yield the sequence (1, 233419, 233420, 466839, 700259, 1167098, 1867357, 3034455, 4901812, 7936267, 12838079, 20774346, 33612425, 54386771, 87999196, 142385967, ...) where a nine-digits anagram is reached.

M. F. Hasler, Table of n, a(n) for n = 1..46494 (full sequence), Jan 09 2020
Patrick De Geest, Nine Digits Digressions
M. F. Hasler, Graph of A034587, n = 1..750767 (full sequence), Jan 10 2020

Cf. A034587 (full sequence), A034589 (lucky numbers), A034306 (palindromes).

select( is_A034587, primes(22222)) \\ or, if a vector A034587 is available:
select(isprime, A034587) \\ e.g., using b034587.txt. - M. F. Hasler, Jan 06 2020

Intersection of A000040 and A034587.

Edited and offset changed to 1 by M. F. Hasler, Jan 06 2020

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

Original entry on oeis.org

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

Patrick De Geest, Oct 15 1998

"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

			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.

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

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).

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

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

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

cp's OEIS Frontend

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

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A034588 Primes p such that the Fibonacci iterations starting with (1, p) lead to a "nine digits anagram".

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

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PARI

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