A308075 - OEIS

A308075

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.

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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

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

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

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

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

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).

LINKS

Jean-Marc Falcoz, Table of n, a(n) for n = 1..1502

Rémy Sigrist, Logarithmic scatterplot of the first 1000000 terms

Rémy Sigrist, Scatterplot of the digital sums of the first 1000000 terms

Rémy Sigrist, PARI program for A308075

EXAMPLE

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

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

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

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

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

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