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

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, …
S = 1,  ,  ,  ,14, 6, (7), 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,1(5), 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,1 ,1(4), 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,1 ,(1) , 50, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, …
S = 1,  ,  ,  ,14, 6,  ,(1) ,  , 60, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, …
Etc.

Crossrefs

Cf. A000027.

Sequence in context: A294899 A118780 A220672 * A051655 A048932 A329022

Adjacent sequences: A353117 A353118 A353119 * A353121 A353122 A353123

Keyword

base,nonn

Author

Eric Angelini and Carole Dubois, Apr 24 2022

Status

approved