A381081 Lexicographically earliest sequence of distinct positive integers such that the string value of a(n) begins with a divisor of a(n-1).

1, 10, 2, 11, 12, 3, 13, 14, 7, 15, 5, 16, 4, 17, 18, 6, 19, 100, 20, 21, 30, 22, 23, 101, 102, 24, 8, 25, 50, 26, 27, 9, 31, 103, 104, 28, 29, 105, 32, 40, 41, 106, 53, 107, 108, 33, 34, 109, 110, 51, 35, 52, 42, 36, 37, 111, 38, 112, 43, 113, 114, 39, 115, 54, 60, 44, 45, 55, 56, 46, 116, 47, 117, 90, 57, 118, 59, 119, 70, 58, 120, 48, 49, 71, 121, 122

Offset: 1

Author

Scott R. Shannon, Feb 13 2025

Keywords

• nonn
• base
• look

Comments

The sequence contains many fixed points, these beginning 1, 22, 23, 40, 41, 52, 199, 1936, 1937, 1938, 1939, ... .

Examples

			a(2) = 10 as the only divisor of a(1) = 1 is 1, and 10 is the smallest unused number to begin with 1.
a(43) = 53 as a(42) = 106 whose divisors are 1, 2, 53, 106, and 53 is the smallest unused number to begin with 53 - all other smaller numbers beginning with 1 and 2 have been used. This is the first term to differ from A248024.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..10000
• Scott R. Shannon, Image of the first 150000 terms. The green line is a(n) = n.

Crossrefs

Cf. A027750, A248024, A000030.