A330760 a(n) is n transformed by the "successive Oware operation" (see the Comments and Example sections).

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 21, 22, 32, 33, 43, 44, 54, 55, 20, 21, 31, 32, 42, 43, 53, 54, 64, 65, 21, 31, 32, 42, 43, 53, 54, 64, 65, 75, 31, 41, 42, 52, 53, 63, 64, 74, 75, 85, 41, 42, 52, 53, 63, 64, 74, 75, 85, 86, 51, 52, 62, 63, 73, 74, 84, 85, 95, 96, 52, 62, 63, 73, 74, 84, 85, 95, 96, 106, 62, 72

Offset: 1

Author

Eric Angelini and Jean-Marc Falcoz, Dec 29 2019

Keywords

• base
• nonn

Comments

To perform a "successive Oware operation" on n we must see the digits of n as a succession of numbers (539 is seen as the succession 5;3;9). We then replace the leftmost number of n with 0 and then "distribute" the (former) value of that number on all numbers, by increasing by 1 the following numbers ("wrapping" around, if necessary, to start over with the first number after the last has been increased). The same task is done with the second number of the result, then the third number of the last result, etc. until the rightmost number of the end result has been transformed. So, if n has k digits, the Oware operation will be done k times altogether.

Examples

			The Oware operation on 539 transforms first 539 into the numbers 5;3;9. It consists then of taking the 5 (and making this number zero) and then increase 5 times the subsequent numbers in a cyclic manner: 3->4; 9->10; 0->1; 4->5; 10->11, which yields the three numbers 1;5;11. The Oware operation is then repeated with 5 (the second number of the result) which turns 1;5;11 into 3;1;13. The last Oware operation is with 13, the rightmost number of the last result, which turns 3;1;13 into 8;5;4. Thus a(539) = 854.
		

Crossrefs

Cf. A216476 (number of iterations of the "Oware" operation until the initial position n is reproduced), A306564 (record values in A216476).