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A110623 Shadow of N (natural numbers), also of Champernowne's shadow. 1
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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

See Definition 7 in the Halbeisen-Hungerbuehler article in A000522 for a definition of the shadow transformation.

LINKS

Table of n, a(n) for n=1..48.

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

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 *)

CROSSREFS

Cf. A007376, A000027, A033307.

Sequence in context: A295327 A179202 A159975 * A163674 A280062 A132947

Adjacent sequences:  A110620 A110621 A110622 * A110624 A110625 A110626

KEYWORD

base,easy,nonn,uned

AUTHOR

Alexandre Wajnberg and Eric Angelini, Sep 14 2005

EXTENSIONS

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

STATUS

approved

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Last modified October 17 21:24 EDT 2018. Contains 316293 sequences. (Running on oeis4.)