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Search: id:A007376
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| A007376 |
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The almost-natural numbers: write n in base 10 and juxtapose digits.
(Formerly M0469)
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+0
59
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| 1, 2, 3, 4, 5, 6, 7, 8, 9, 1, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 9, 2, 0, 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7, 2, 8, 2, 9, 3, 0, 3, 1, 3, 2, 3, 3, 3, 4, 3, 5, 3, 6, 3, 7, 3, 8, 3, 9, 4, 0, 4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6, 4, 7, 4, 8, 4, 9, 5, 0, 5, 1, 5, 2, 5, 3, 5, 4, 5, 5, 5, 6, 5, 7
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Also called the Barbier infinite word.
a(n) = A162711(n,1); A136414(n) = 10*a(n) + a(n+1). [From Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jul 11 2009]
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REFERENCES
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J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, p. 114.
R. Honsberger, Mathematical Chestnuts from Around the World, MAA, 2001; see p. 163.
M. Kraitchik, Mathematical Recreations. Dover, NY, 2nd ed., 1953, p. 49.
48th Putnam Competition, Problem A2, Math. Mag., 61 (1988), 131-134.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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Robert G. Wilson v, Table of n, a(n) for n=1..100000
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MAPLE
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c:=proc(x, y) local s: s:=proc(m) nops(convert(m, base, 10)) end: if y=0 then 10*x else x*10^s(y)+y: fi end: b:=proc(n) local nn: nn:=convert(n, base, 10):[seq(nn[nops(nn)+1-i], i=1..nops(nn))] end: A:=0: for n from 1 to 75 do A:=c(A, n) od: b(A); # c concatenates 2 numbers while b converts a number to the sequence of its digits - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jul 27 2006
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MATHEMATICA
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Flatten[IntegerDigits/@Range[57]] (* Or *)
a[n_] := Block[{m = 0, d = n, i = 1, l, p}, While[m <= d, l = m; m = 9i*10^(i - 1) + l; i++ ]; i--; p = Mod[d - l, i]; q = Floor[(d - l)/i] + 10^(i - 1); If[p != 0, IntegerDigits[q][[p]], Mod[q - 1, 10]]]; Table[ a[n], {n, 1, 105}]
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CROSSREFS
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Considered as a sequence of digits, this is the same as the decimal expansion of the Champernowne constant, A033307. See that entry for a formula for a(n), further references, etc.
Cf. A054632, A023103.
For "decimations" see A127050 A127353 A127414 A127508 A127584 A127734 A127794 A127950 A128178 A128211 A128359 A128423 A128475 A128881.
Sequence in context: A084044 A048379 A033307 this_sequence A001073 A076313 A055017
Adjacent sequences: A007373 A007374 A007375 this_sequence A007377 A007378 A007379
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KEYWORD
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base,easy,nice,nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)
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