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%I #15 Jun 15 2021 11:03:47
%S 1,3,10,28,309,317,601,606,696,700,752,787,1147,1434,1481,1494,2020,
%T 2026,2050,2059,2136,2193,4663,4756,4825,4924,4983,5557,5653,12620,
%U 12682,13454,13494,13570,14200,14553,14607,14682,14776,15347,15385
%N Shadow of Euler's constant exp(1).
%C The shadow of the decimal expansion of a constant (here: A001113) is defined as a sequence of integers such that (i) the concatenation of the first differences reproduces the decimal expansion, (ii) no integer appears more than once in the sequence or its first differences, (iii) at each step the smallest possible number of digits of the constant is swallowed to define the first differences, not leaving a leading zero behind.
%e The first line hereunder is the sequence, the second line gives the first differences:
%e 1.3.10..28...309.317...601.606..696.700..752..787...1147...1434..1481...
%e .2.7..18..281...8...284...5...90...4...52...35...360....287....47 <-- "e" shadow
%e e = 2.71828182845904523536028747135266249775724709369995...
%t a[1] = 1; a[n_] := a[n] = Block[{c = RealDigits[E, 10, 300][[1]], 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, 41}] (* _Robert G. Wilson v_ *)
%Y Cf. A001113, A110557, A110621, A110623.
%K base,easy,nonn
%O 1,2
%A _Eric Angelini_ and _Alexandre Wajnberg_, Sep 14 2005
%E Corrected and extended by _Robert G. Wilson v_, Oct 10 2005
%E Comment expanded by _R. J. Mathar_, Jun 15 2010
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