

A306807


An irregular fractal sequence: underline a(n) iff the absolute difference a(n1)  a(n) is prime; all underlined terms rebuild the starting sequence.


1



1, 2, 3, 1, 5, 2, 6, 3, 1, 7, 5, 2, 8, 6, 3, 1, 9, 7, 5, 2, 10, 8, 6, 3, 1, 11, 9, 7, 5, 2, 12, 10, 8, 6, 3, 1, 13, 11, 9, 7, 5, 2, 14, 12, 10, 8, 6, 3, 1, 15, 13, 11, 9, 7, 5, 2, 16, 14, 12, 10, 8, 6, 3, 1, 17, 15, 13, 11, 9, 7, 5, 2, 18, 16, 14, 12, 10, 8, 6, 3, 1, 19, 17, 15, 13, 11, 9, 7, 5, 2, 20, 18, 16, 14, 12, 10, 8, 6, 3, 1
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OFFSET

1,2


COMMENTS

The sequence S starts with a(1) = 1 and a(2) = 2. S is extended by duplicating the first term A among the not yet duplicated terms, under the condition that the absolute difference a(n1)  a(n) is prime. If this is not the case, we then extend S with the smallest integer X not yet present in S such that the absolute difference a(n1)  a(n) is not prime. S is the lexicographically earliest sequence with this property.


LINKS

JeanMarc Falcoz, Table of n, a(n) for n = 1..10002


EXAMPLE

S starts with a(1) = 1 and a(2) = 2
Can we duplicate a(1) to form a(3)? No, as a(2)  a(3) would be 1 and 1 is not prime. We thus extend S with the smallest integer X not yet in S such that a(2)  X is not prime. We get a(3) = 3.
Can we duplicate a(1) to form a(4)? Yes, as a(3)  a(4) = 2, which is prime. We get a(4) = 1.
Can we duplicate a(2) to form a(5)? No, as a(4)  a(5) would be 1 and 1 is not prime. We thus extend S with the smallest integer X not yet in S such that a(4)  X is not prime; we get a(5) = 5.
Can we duplicate a(2) to form a(6)? Yes, as a(6)  a(5) = 3, which is prime; we get a(6) = 2.
Etc.


CROSSREFS

Cf. A306803 (obtained by replacing the absolute difference by the sum in the definition).
Sequence in context: A075014 A304880 A086686 * A021816 A055023 A323071
Adjacent sequences: A306804 A306805 A306806 * A306808 A306809 A306810


KEYWORD

base,nonn,look


AUTHOR

Alexandre Wajnberg and Eric Angelini, Mar 11 2019


STATUS

approved



