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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.
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
1,3
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
EXAMPLE
a(10)=3 since it shares a digit (3) with a(8)=13, and shares no digit with a(9)=24.
PROG
(PARI) See Cano link.
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Enrique Navarrete, Apr 20 2018
STATUS
approved