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%I #15 Apr 08 2023 11:44:17
%S 3,1,2,6,4,5,9,7,8,22,30,40,20,23,24,25,26,27,33,34,35,10,11,13,14,15,
%T 16,17,18,28,44,19,12,21,29,41,42,45,51,32,36,50,52,31,37,38,39,53,61,
%U 43,46,47,60,62,48,49,63,64,71,54,55,57,58,70,72,59,90,73,81,56,65,66
%N Smallest positive integer a(n) not yet in the sequence and sharing no digit with n or (n+1) in its decimal representation.
%C Record values: 3, 6, 9, 22, 30, 40, 44, 45, 51, 52, 53, 61, 62, 63, 64, 71, 72, 90, 91, 100, 111, 112, 222, 223, 224, 225, 226, 300, 400, 404, 500, 505, 506, 507, 600, 601, 602, 700, 701, 702, 703, 800, 811, 900, 901, 902, 1000, 1111, 1112, 1113, 1114, 1117, 1121, 2222, 3000, 3003, 3004, 3005, 3333, 3334, 4444, 4445, 4446, 4447, 5000, 5005, 5555, 6000, 6006, 6007, 6008, 6009, 6060, 6066, 6067, 6068, 6069, 6070, 6076, 6111, 7000, 7002, 7007, 7008, 7009, 7010, 7011, 8000, 8001, 8002, 8008, 8010, 8011, 8012, 8111, 9000, 9001, 9002, 10000, 11111, 11112, 11113, 11114, 11115, 20000, 20002, 20003, 20004, 22222, 33333, 33334, 33335, 40000, 40004, 40005, 40006, 40007, 40040, ..., . - _Robert G. Wilson v_, Sep 25 2010
%C Sequence has 12345677 terms, ending with a(12345677) = 9900000900009. - _Michael S. Branicky_, Apr 08 2023
%H Robert G. Wilson v, <a href="/A171072/b171072.txt">Table of n, a(n) for n = 1..10000</a>.
%H Michael S. Branicky, <a href="/A171072/a171072.py.txt">Python program</a>
%t f[s_List] := Block[{k = 1, len = Length@ s}, id = Union@ Flatten[ IntegerDigits /@ {len + 1, len + 2}]; While[ MemberQ[s, k] || Intersection[ id, IntegerDigits@ k] != {}, k++ ]; Append[s, k]]; Nest[f, {}, 72] (* _Robert G. Wilson v_, Sep 25 2010 *)
%o (Python) # see linked program generating full sequence
%Y Cf. A160015. - _Robert G. Wilson v_, Sep 25 2010
%K nonn,base,fini
%O 1,1
%A _N. J. A. Sloane_, Sep 06 2010, based on an email from _Eric Angelini_, Jun 30 2010
%E a(25) onwards from _Robert G. Wilson v_, Sep 25 2010
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