A110623 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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

(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").

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