A303294 a(n) is the least positive integer not yet in the sequence which shares a digit with either a(n-3) or a(n-2) (or with both), but shares no digit with a(n-1); a(1)=0, a(2)=1, a(3)=2.

0, 1, 2, 10, 22, 11, 20, 13, 24, 3, 4, 12, 30, 14, 23, 15, 26, 5, 6, 21, 35, 16, 25, 17, 28, 7, 8, 27, 18, 29, 31, 9, 32, 19, 33, 41, 36, 40, 37, 42, 38, 44, 39, 45, 63, 47, 50, 34, 51, 43, 52, 46, 53, 48, 55, 49, 56, 74, 58, 60, 54, 61, 57, 62, 59

Offset: 1

Author

Enrique Navarrete, Apr 20 2018

Keywords

• nonn
• base

Comments

Apparently there exist only 5 pairs of consecutive integers belonging this sequence, a(k+1)-a(k)=1 for k in (1,2,10,18,26). Respectively those pairs are: (0;1), (1;2), (3;4), (5;6), and (7;8).

It seems that a(j)=j only for j in (12,14,31,53,55,60,71,73,75,82,84,95,102). - R. J. Cano, Apr 22 2018

Examples

			a(10)=3 since it shares a digit (3) with a(8)=13, and shares no digit with a(9)=24.
		

Links

• R. J. Cano, Table of n, a(n) for n = 1..10000
• R. J. Cano, A sequencer program in PARI.

Crossrefs

Cf. A286890, A300907, A302566, A302388.

Programs

PARI

See Cano link.