Horizontal graph (and more)
Every digit d of the sequence S is at the vertex of an infinite graph that visits all integers of S . This digit d is linked by d edges to the graph. S is the lexicographically earliest sequence with this property. I hope S starts like that: S = 1, 2, 3, 4, 5, 6, 7, 8, 9, 62, 22, 23, 32, 24, 42, 25, 52, 26, 63, 33, 34, 43, 35, 53, 36, 64, 44, 45, 54, 46, 65, 55, 56, 66, 67, 73, 37, 74, 47, 75, 57, ... The hereunder image will show what we mean. The first line alternates the blue and red colors for the integers of S The second line splits the digits of the integers > 9 The third line shows the number of edges involving each digit d (those are the small numbers between the split digits) Every “big” digit d is surrounded by two “small” digits whose sum is d – this sum being the total number of edges involving d : I don't know if the metaphor of the graph is appropriate for the mechanism ruling S. Neither do I know whether the words “vertex” and “edge” were used corre
