A120442 P-positions of John H. Conway's "Digit Deletions" game from "On Numbers and Games". Each number is the smallest positive integer that cannot be reduced to an earlier number in the sequence, by performing one of the following two operations: (1) changing one digit to a smaller digit (but not changing the leading digit to 0), or (2) deleting a 0 and all subsequent digits.

1, 11, 20, 32, 43, 54, 65, 76, 87, 98, 111, 120, 132, 143, 154, 165, 176, 187, 198, 201, 210, 222, 233, 244, 255, 266, 277, 288, 299, 300, 312, 321, 334, 345, 353, 367, 378, 386, 402, 413, 424, 431, 440, 456, 468, 475, 489, 497, 503, 514

Offset

1,2

Comments

The sequence is base-dependent, but notice that each number in a given base's sequence has a correspondent in all higher bases (the number with the same digit representation). The smallest n-digit number in the sequence is always a repunit.

References

John H. Conway, On Numbers and Games, 2nd Edition, pp. 190-192.

Links

Table of n, a(n) for n=1..50.

Example

201 is in the sequence because every number it may be reduced to (101, 2, 200) is not in the sequence: 101 and 2 both reduce to 1 and 200 reduces to 20.

Crossrefs

Sequence in context: A044435 A302563 A011753 * A059407 A109376 A100038

Adjacent sequences: A120439 A120440 A120441 * A120443 A120444 A120445

Keyword

base,easy,nonn

Author

Trevor Green (green(AT)math.usask.ca), Jul 18 2006

Status

approved