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Lexicographically earliest sequence of distinct positive terms with an associate sequence t such that t(0) = 0, and for any n > 0, at least one of t(n-1) - a(n) or t(n-1) + a(n) is a palindrome; in case t(n-1) - a(n) is a palindrome, set t(n) = t(n-1) - a(n), otherwise set t(n) = t(n-1) + a(n).
4

%I #14 Dec 16 2019 02:19:06

%S 1,2,3,4,5,6,8,7,18,11,9,20,13,24,22,10,21,14,25,26,15,16,27,28,17,19,

%T 30,29,40,33,44,46,35,36,47,48,37,38,49,50,39,41,52,51,62,45,12,32,43,

%U 23,34,54,60,31,61,71,81,63,53,42,55,57,68,66,72,70,79

%N Lexicographically earliest sequence of distinct positive terms with an associate sequence t such that t(0) = 0, and for any n > 0, at least one of t(n-1) - a(n) or t(n-1) + a(n) is a palindrome; in case t(n-1) - a(n) is a palindrome, set t(n) = t(n-1) - a(n), otherwise set t(n) = t(n-1) + a(n).

%C This sequence is a variant of A329544.

%H Rémy Sigrist, <a href="/A330401/b330401.txt">Table of n, a(n) for n = 1..10000</a>

%H Rémy Sigrist, <a href="/A330401/a330401_1.gp.txt">PARI program for A330401</a>

%e The first terms, alongside t(n), are:

%e n a(n) t(n)

%e -- ---- ----

%e 0 N/A 0

%e 1 1 1

%e 2 2 3

%e 3 3 0

%e 4 4 4

%e 5 5 9

%e 6 6 3

%e 7 8 11

%e 8 7 4

%e 9 18 22

%e 10 11 11

%e 11 9 2

%e 12 20 22

%o (PARI) See Links section.

%Y See A330402 and A330403 for similar sequences.

%Y Cf. A002113, A329544, A330420 (running totals).

%K nonn,base

%O 1,2

%A _Rémy Sigrist_, Dec 13 2019