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A306807 An irregular fractal sequence: underline a(n) iff the absolute difference |a(n-1) - a(n)| is prime; all underlined terms rebuild the starting sequence. 1

%I

%S 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,

%T 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,

%U 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

%N An irregular fractal sequence: underline a(n) iff the absolute difference |a(n-1) - a(n)| is prime; all underlined terms rebuild the starting sequence.

%C 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(n-1) - 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(n-1) - a(n)| is not prime. S is the lexicographically earliest sequence with this property.

%H Jean-Marc Falcoz, <a href="/A306807/b306807.txt">Table of n, a(n) for n = 1..10002</a>

%e S starts with a(1) = 1 and a(2) = 2

%e 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.

%e Can we duplicate a(1) to form a(4)? Yes, as |a(3) - a(4)| = 2, which is prime. We get a(4) = 1.

%e 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.

%e Can we duplicate a(2) to form a(6)? Yes, as |a(6) - a(5)| = 3, which is prime; we get a(6) = 2.

%e Etc.

%Y Cf. A306803 (obtained by replacing the absolute difference by the sum in the definition).

%K base,nonn,look

%O 1,2

%A _Alexandre Wajnberg_ and _Eric Angelini_, Mar 11 2019

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Last modified June 14 13:09 EDT 2021. Contains 345025 sequences. (Running on oeis4.)