

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
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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 HalbeisenHungerbuehler 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



