%I A110623
%S A110623 1,13,16,20,25,31,38,46,55,65,76,197,511,526,687,758,839,1759,1761,1883,
%T A110623 1906,1930,2182,2244,2316,2398,3328,3641,3874,3908,3943,3979,4016,4399,
%U A110623 5339,5380,5422,5465,5509,5554,6018,6092,6176,7126,7177,7229,7282,7336
%N A110623 Shadow of N (natural numbers), also of Champernowne's shadow.
%C A110623 First differences are N's shadow. Never twice the same integer in sequence 
               or first differences (except the starting "1").
%e A110623 The first line hereunder is the sequence, the second line gives the first 
               differences:
%e A110623 1..13.16.20.25.31.38.46.55..65..76...197..228..269..311 ...
%e A110623 .12..3..4..5..6..7..8..9..10..11..121...31...41...51... <-- N's shadow
%t A110623 a[1] = 1; a[n_] := a[n] = Block[{c = Flatten[ IntegerDigits /@ Range[150]], 
               k = 1, t = Table[a[i], {i, n - 1}]}, d = Drop[t, 1] - Drop[t, -1]; 
               b = Drop[c, Length[ Flatten[ IntegerDigits /@ d]]]; e = Union[ Join[t, 
               d]]; While[f = FromDigits[ Take[b, k]]; Position[e, f] != {} || b[[k 
               + 1]] == 0, k++ ]; f + a[n - 1]]; Table[ a[n], {n, 48}] (* Robert 
               G. Wilson v *)
%Y A110623 Cf. A007376, A000027, A033307.
%Y A110623 Sequence in context: A153051 A064805 A159975 this_sequence A163674 A132947 
               A056663
%Y A110623 Adjacent sequences: A110620 A110621 A110622 this_sequence A110624 A110625 
               A110626
%K A110623 base,easy,nonn,uned
%O A110623 1,2
%A A110623 Alexandre Wajnberg (alexandre.wajnberg(AT)skynet.be) & Eric Angelini 
               (eric.angelini(AT)kntv.be), Sep 14 2005
%E A110623 Corrected and extended by Robert G. Wilson v (rgwv(at)rgwv.com), Oct 
               10 2005