

A132075


A conjectured permutation of the positive integers such that for every n, a(n) is the largest number among a(1), a(2), ..., a(n) that when added to a(n+1) gives a prime.


3



1, 2, 3, 4, 7, 6, 5, 14, 9, 10, 13, 16, 15, 8, 11, 20, 17, 12, 19, 24, 23, 18, 25, 22, 21, 26, 27, 34, 33, 28, 31, 30, 29, 32, 35, 36, 37, 46, 43, 40, 39, 44, 45, 38, 41, 42, 47, 50, 59, 54, 55, 58, 51, 62, 65, 48, 61, 52, 57, 56, 53, 60, 49, 64, 63, 68, 69, 70, 67, 72, 77, 80, 71, 66, 73, 78, 79, 84, 83, 90, 89, 74, 75, 76, 81, 82, 85, 88, 93, 86, 95, 104, 107, 92
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OFFSET

1,2


COMMENTS

The terms are defined as follows. Start by choosing the initial terms: 1, 2, 3. Then write the rows of table A088643 backwards but always leave off the last three quarters of the terms. This gives: [], [], [], [1], [1], [1], [1], [1, 2], [1, 2], [1, 2], [1, 4], [1, 4, 3,], [1, 4, 3] etc. Then build the sequence up by repeatedly choosing the first such truncated row that extends the terms already chosen. [Edited by Peter Munn, Aug 19 2021]
It is not until the 26th truncated row  [1, 2, 3, 4, 7, 6]  that the initial list is extended at all. It is unclear whether this process can be continued indefinitely, although I have verified by computer that it generates a sequence of at least 2000 terms. Conjecturally: (1) the sequence is infinite, (2) it is the unique sequence containing infinitely many complete rows of table A088643, and (3) for every n > 0 there exists N > 0 such that the first n terms of this sequence are contained in every row of table A088643 from the Nth onwards.
Maybe the idea could be expressed more concisely by defining this sequence as the limit of the reversed rows of A088643?  M. F. Hasler, Aug 04 2021
It seems we do not know of an existence proof for the limit of the reversed rows of A088643.  Peter Munn, Aug 19 2021


LINKS

Table of n, a(n) for n=1..94.
Peter Munn, Illustration of the relationship between A088643, this sequence and A255312.


CROSSREFS

Cf. A088643.
Sequence in context: A292959 A292957 A338644 * A265364 A265363 A319651
Adjacent sequences: A132072 A132073 A132074 * A132076 A132077 A132078


KEYWORD

easy,nonn


AUTHOR

Paul Boddington, Oct 30 2007, Mar 06 2010


EXTENSIONS

Name edited by Peter Munn, Aug 19 2021


STATUS

approved



