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 A108912 Shadow of Euler's constant exp(1). 0
 1, 3, 10, 28, 309, 317, 601, 606, 696, 700, 752, 787, 1147, 1434, 1481, 1494, 2020, 2026, 2050, 2059, 2136, 2193, 4663, 4756, 4825, 4924, 4983, 5557, 5653, 12620, 12682, 13454, 13494, 13570, 14200, 14553, 14607, 14682, 14776, 15347, 15385 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS 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. LINKS EXAMPLE The first line hereunder is the sequence, the second line gives the first differences: 1.3.10..28...309.317...601.606..696.700..752..787...1147...1434..1481... .2.7..18..281...8...284...5...90...4...52...35...360....287....47 <-- "e" shadow e = 2.71828182845904523536028747135266249775724709369995... MATHEMATICA 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 *) CROSSREFS Cf. A001113, A110557, A110621, A110623. Sequence in context: A246974 A278294 A260811 * A055336 A092325 A130218 Adjacent sequences:  A108909 A108910 A108911 * A108913 A108914 A108915 KEYWORD base,easy,nonn AUTHOR Eric Angelini & Alexandre Wajnberg , Sep 14 2005 EXTENSIONS Corrected and extended by Robert G. Wilson v, Oct 10 2005 Comment expanded by R. J. Mathar, Jun 15 2010 STATUS approved

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Last modified August 10 14:50 EDT 2020. Contains 336381 sequences. (Running on oeis4.)