A367635 Variation of the "Comma sequence" A121805: allow one or more digits from both a(n-1) and a(n) to form the magnitude of the difference |a(n) - a(n-1)|, always choosing the minimum possible distinct value for a(n).

1, 12, 35, 94, 135, 78, 159, 63, 30, 15, 72, 48, 129, 36, 399, 306, 244, 202, 181, 170, 85, 32, 6, 73, 104, 59, 150, 75, 23, 58, 139, 45, 499, 405, 352, 76, 8, 97, 25, 83, 49, 140, 70, 64, 22, 46, 107, 34, 82, 57, 128, 44, 2, 24, 71, 56, 117, 43, 81, 65, 14, 60, 55, 106, 42, 20, 10, 5, 61, 47

Offset: 1

Author

Scott R. Shannon, Nov 25 2023

Keywords

• nonn
• base
• fini
• full

Comments

The sequence is finite; after 206 terms 9 is reached which only has one possible following term 100, but 100 has already appeared. The largest difference between terms is 910, from a(151) = 99 to a(152) = 1009, the later being the largest term of the sequence.

Examples

			a(6) = 78 as a(5) = 135, and |78 - 135| = 57 which can be formed from one digit of 135 and one digit of 78.
a(15) = 399 as a(14) = 36, and |399 - 36| = 363 which can be formed from two digits of 36 and one digit of 399. This is the first term whose difference with the previous term uses more than two digits.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..206

Crossrefs

Cf. A121805, A367363, A367645.