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Search: id:A110623
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| A110623 |
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Shadow of N (natural numbers), also of Champernowne's shadow. |
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+0
1
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| 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; listen)
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OFFSET
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1,2
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COMMENT
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First differences are N's shadow. Never twice the same integer in sequence or first differences (except the starting "1").
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EXAMPLE
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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
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MATHEMATICA
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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 *)
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CROSSREFS
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Cf. A007376, A000027, A033307.
Sequence in context: A153051 A064805 A159975 this_sequence A163674 A132947 A056663
Adjacent sequences: A110620 A110621 A110622 this_sequence A110624 A110625 A110626
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KEYWORD
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base,easy,nonn,uned
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AUTHOR
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Alexandre Wajnberg (alexandre.wajnberg(AT)skynet.be) & Eric Angelini (eric.angelini(AT)kntv.be), Sep 14 2005
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EXTENSIONS
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Corrected and extended by Robert G. Wilson v (rgwv(at)rgwv.com), Oct 10 2005
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