

A034588


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


4



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
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OFFSET

1,1


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


LINKS



FORMULA



EXAMPLE

Starting with (1, 233419), Fibonacci iterations x(n+1) = x(n) + x(n1) yield the sequence (1, 233419, 233420, 466839, 700259, 1167098, 1867357, 3034455, 4901812, 7936267, 12838079, 20774346, 33612425, 54386771, 87999196, 142385967, ...) where a ninedigits anagram is reached.


PROG

(PARI) select( is_A034587, primes(22222)) \\ or, if a vector A034587 is available:


CROSSREFS



KEYWORD

nonn,base,fini


AUTHOR



EXTENSIONS



STATUS

approved



