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

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

Author

Patrick De Geest, Oct 15 1998

Keywords

• nonn
• base
• fini

Comments

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

Examples

			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.
		

Links

• 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

Crossrefs

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

Programs

PARI

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

Formula

Intersection of A000040 and A034587.

Extensions

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