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%I A110623 #28 Sep 17 2019 10:31:49
%S A110623 1,13,16,20,25,31,38,46,55,65,76,197,511,526,687,758,839,1759,1761,
%T A110623 1883,1906,1930,2182,2244,2316,2398,3328,3641,3874,3908,3943,3979,
%U A110623 4016,4399,5339,5380,5422,5465,5509,5554,6018,6092,6176,7126,7177,7229,7282,7336
%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").
%H A110623 Petros Hadjicostas, <a href="/A110623/b110623.txt">Table of n, a(n) for n = 1..130</a>
%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 (which, when concatenated, gives A033307)
%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_, Oct 10 2005 *)
%Y A110623 Cf. A000027, A007376, A033307.
%K A110623 base,easy,nonn
%O A110623 1,2
%A A110623 _Alexandre Wajnberg_ and _Eric Angelini_, Sep 14 2005
%E A110623 Corrected and extended by _Robert G. Wilson v_, Oct 10 2005

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