A110623 Shadow of N (natural numbers), also of Champernowne's shadow.

1, 13, 16, 20, 25, 31, 38, 46, 55, 65, 76, 197, 511, 526, 687, 758, 839, 1759, 1761, 1883, 1906, 1930, 2182, 2244, 2316, 2398, 3328, 3641, 3874, 3908, 3943, 3979, 4016, 4399, 5339, 5380, 5422, 5465, 5509, 5554, 6018, 6092, 6176, 7126, 7177, 7229, 7282, 7336

Offset

1,2

Comments

First differences are N's shadow. Never twice the same integer in sequence or first differences (except the starting "1").

Links

Petros Hadjicostas, Table of n, a(n) for n = 1..130

Example

The first line hereunder is the sequence, the second line gives the first differences:
1..13.16.20.25.31.38.46.55..65..76...197..228..269..311 ...
.12..3..4..5..6..7..8..9..10..11..121...31...41...51... <-- N's shadow (which, when concatenated, gives A033307)

Mathematica

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 *)

Crossrefs

Cf. A000027, A007376, A033307.

Sequence in context: A179202 A159975 A350300 * A163674 A280062 A132947

Adjacent sequences: A110620 A110621 A110622 * A110624 A110625 A110626

Keyword

base,easy,nonn

Author

Alexandre Wajnberg and Eric Angelini, Sep 14 2005

Extensions

Corrected and extended by Robert G. Wilson v, Oct 10 2005

Status

approved