A277558 A variation on Recamán's sequence (A005132): to get a(n), we first try to subtract n from a(n-1): a(n) = a(n-1)-n if positive and not already in the sequence; if not then a(n) = a(n-1)+n-i, where i >= 0 is the smallest number such that a(n-1)+n-i has not already appeared.

0, 1, 3, 6, 2, 7, 13, 20, 12, 21, 11, 22, 10, 23, 9, 24, 8, 25, 43, 62, 42, 63, 41, 18, 40, 15, 39, 66, 38, 67, 37, 68, 36, 69, 35, 70, 34, 71, 33, 72, 32, 73, 31, 74, 30, 75, 29, 76, 28, 77, 27, 78, 26, 79, 133, 188, 132, 189, 131, 190, 130, 191, 129, 192

Offset

0,3

Comments

Is it ever impossible to extend the sequence -- meaning there is no number less than a(n-1)+n which has not appeared?

After 10^11 terms, the smallest number which has not appeared is 609790506.

Links

Benjamin Chaffin, Table of n, a(n) for n = 0..10000

Example

a(23) = 18. To get a(24) we try 18-24, but that is negative; so we try 18+24 = 42, but 42 has already appeared; so we try 18+24-1, but 41 has also already appeared; so we try 18+24-2. 40 is positive and has not yet appeared, and so a(24) = 40.

Crossrefs

Cf. A005132, A064387 (chooses a(n-1)+n+i instead of a(n-1)+n-i).

Sequence in context: A074170 A076543 A274648 * A350578 A335299 A005132

Adjacent sequences: A277555 A277556 A277557 * A277559 A277560 A277561

Keyword

nonn

Author

Benjamin Chaffin, Oct 19 2016

Status

approved