A333774 a(0) = 0; for n > 0, a(n) = the smallest positive integer not yet appearing in the sequence such that a(n-1) + a(n) contains as a substring either a(n-1) or a(n).

0, 1, 9, 10, 2, 18, 100, 3, 20, 4, 30, 5, 40, 6, 50, 7, 60, 8, 70, 200, 11, 99, 300, 12, 108, 972, 107, 963, 106, 954, 105, 945, 104, 936, 103, 927, 102, 918, 101, 909, 1000, 13, 117, 1053, 116, 1044, 115, 1035, 114, 1026, 113, 1017, 112, 1008, 111, 999, 110, 990, 109, 981, 2000, 14

Offset: 0

Author

Scott R. Shannon, Apr 05 2020

Keywords

• nonn
• base

Examples

			a(1) = 1 as a(0) = a(1) = 0 + 1 = 1 which contains '1' as a substring.
a(2) = 9 as a(1) + a(2) = 1 + 9 = 10 which contains '1' as a substring.
a(4) = 2 as a(3) + a(4) = 10 + 2 = 12 which contains '2' as a substring
a(49) = 1026 as a(48) + a(49) = 114 + 1026 = 1140 which contains '114' as a substring.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 0..10000
• Rémy Sigrist, PARI program for A333774

Crossrefs

Cf. A333775, A333811, A332795, A332703.

Programs

PARI

See Links section.