A308075 - OEIS

%I #21 Dec 10 2023 18:07:27

%S 1,2,3,5,8,12,14,11,7,9,20,16,18,79,25,27,88,34,36,97,43,45,101,29,49,

%T 110,38,54,200,47,58,699,56,67,789,65,76,798,74,85,879,83,94,888,92,

%U 139,897,119,148,969,128,157,978,137,166,987,146,175,996,155,184,1001,69,89,1010,78,98,1100,87,179,2000,96,188,5999,159,197,6899

%N Lexicographically earliest sequence of distinct positive integers such that the sum of the digits of a(n) is either the sum of all the digits of a(n-1) and a(n+1), or is the absolute difference |(sum of digits of a(n-1)) - (sum of digits of a(n+1))|, for n > 1.

%C To get the "New sequence" below, replace all terms by the sum of their digits:

%C This seq = 1,2,3,5,8,12,14,11,7,9,20,16,18,79,25,27,88,...

%C New  seq = 1,2,3,5,8, 3, 5, 2,7,9, 2, 7, 9,16, 7, 9,16,...

%C We see that every term of the "New sequence" is either the sum of its two adjacent terms, or their absolute difference.

%C This sequence may not be a permutation of the positive integers as the number 10 does not appear among the first 1000000 terms (according to Rémy Sigrist).

%H Jean-Marc Falcoz, <a href="/A308075/b308075.txt">Table of n, a(n) for n = 1..1502</a>

%H Rémy Sigrist, <a href="/A308075/a308075.png">Logarithmic scatterplot of the first 1000000 terms</a>

%H Rémy Sigrist, <a href="/A308075/a308075_1.png">Scatterplot of the digital sums of the first 1000000 terms</a>

%H Rémy Sigrist, <a href="/A308075/a308075.gp.txt">PARI program for A308075</a>

%e a(2) = 2 is |1-3|;

%e a(3) = 3 is |2-5|;

%e a(4) = 5 is |3-8|;

%e a(5) = 8 is (5+1+2);

%e a(6) = 12 because 12 gives (1+2) = 3 and this 3 is (8-1-4);

%e a(7) = 14 because 14 gives (1+4) = 5 and this 5 is (1+2+1+1);

%e a(8) = 11 because 11 gives (1+1) = 2 and this 2 is |1+4-7|;

%e etc.

%o (PARI) See Links section.

%Y Cf. A007953 (Digital sum (i.e., sum of digits) of n; also called digsum(n)), A307638 (digital sums of this sequence).

%K base,nonn

%O 1,2

%A _Eric Angelini_ and _Jean-Marc Falcoz_, May 11 2019