A108912 Shadow of Euler's constant exp(1).

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

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

Table of n, a(n) for n=1..41.

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 * A350821 A361741 A055336

Adjacent sequences: A108909 A108910 A108911 * A108913 A108914 A108915

Keyword

base,easy,nonn

Author

Eric Angelini and 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