

A291603


Lexicographically earliest sequence of distinct positive terms such that for any n > 0, a(n) is coprime to a(2*n) and to a(2*n+1).


3



1, 2, 3, 5, 7, 4, 8, 6, 9, 10, 11, 13, 15, 17, 19, 23, 25, 14, 16, 21, 27, 12, 18, 20, 22, 26, 28, 24, 29, 30, 31, 32, 33, 34, 36, 37, 39, 35, 41, 38, 40, 43, 44, 47, 49, 53, 55, 51, 57, 45, 59, 61, 63, 65, 67, 71, 73, 42, 46, 77, 79, 48, 50, 69, 75, 52, 56
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OFFSET

1,2


COMMENTS

This sequence has connections with A082746: here a(n) is coprime to a(2*n) and to a(2*n+1), there a(n) is coprime to a(2*n).
This sequence is a permutation of the natural numbers (with inverse A291604 and fixed points A291610):
 the sequence can always be extended with a prime number,
 all prime numbers appear in the sequence, in increasing order,
 for any n, there are infinitely many prime numbers coprime to n, so eventually n will appear in the sequence.


LINKS

Rémy Sigrist, Table of n, a(n) for n = 1..10000
Rémy Sigrist, Scatterplot of the first 10000 terms
Rémy Sigrist, PARI program for A291603
Index entries for sequences that are permutations of the natural numbers


EXAMPLE

a(1) = 1 is suitable.
a(2) must be coprime to a(1) = 1.
a(2) = 2 is suitable.
a(3) must be coprime to a(1) = 1.
a(3) = 3 is suitable.
a(4) must be coprime to a(2) = 2.
a(4) = 5 is suitable.
a(5) must be coprime to a(2) = 2.
a(5) = 7 is suitable.
a(6) must be coprime to a(3) = 3.
a(6) = 4 is suitable.
a(7) must be coprime to a(3) = 3.
a(7) = 8 is suitable.
a(8) must be coprime to a(4) = 5.
a(8) = 6 is suitable.
a(9) must be coprime to a(4) = 5.
a(9) = 9 is suitable.
a(10) must be coprime to a(5) = 7.
a(10) = 10 is suitable.


PROG

See Links section.


CROSSREFS

Cf. A082746, A291604 (inverse), A291610 (fixed points).
Sequence in context: A082196 A292876 A126049 * A082331 A140528 A065037
Adjacent sequences: A291600 A291601 A291602 * A291604 A291605 A291606


KEYWORD

nonn,look


AUTHOR

Rémy Sigrist, Aug 27 2017


STATUS

approved



