A353120 - OEIS

A353120

(a) Write down all the natural integers on a single row S, starting with 1; (b) start reading S from the very beginning of S; (c) if a single digit d stands between two digits having the same parity, lift d and add it to the digit immediately to its right; (d) go back to (a). The sequence is the end result of this procedure.

1, 14, 6, 79, 2, 2, 73, 2, 6, 7, 120, 99, 4, 4, 9, 122, 1, 124, 5, 106, 5, 128, 59, 6, 6, 154, 6, 116, 6, 138, 6, 1, 122, 7, 104, 7, 126, 7, 148, 79, 8, 8, 5140, 3, 124, 9, 146, 9, 168, 9, 100, 9, 104, 1308, 3, 102, 1326, 1128, 7, 104, 1344, 1146, 1348, 9, 164, 1366, 1568, 1104, 1380, 1182, 1384, 1586, 1788, 9

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OFFSET

1,2

LINKS

Table of n, a(n) for n=1..74.

Eric Angelini, Does this sequence unexist?, Personal blog of the author.

EXAMPLE

First successive steps of the procedure (the successive lifted digits are parenthesized, then added to the digit on their right):

S = 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, …

S = 1, (2), 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, …

S = 1, , 5, (4), 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, …

S = 1, , (5), , 9, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, …