Search: id:A007376
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%I A007376 M0469
%S A007376 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,
%T A007376 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,
%U A007376 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
%N A007376 The almost-natural numbers: write n in base 10 and juxtapose digits.
%C A007376 Also called the Barbier infinite word.
%C A007376 a(n) = A162711(n,1); A136414(n) = 10*a(n) + a(n+1). [From Reinhard Zumkeller 
               (reinhard.zumkeller(AT)gmail.com), Jul 11 2009]
%D A007376 J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 
               2003, p. 114.
%D A007376 R. Honsberger, Mathematical Chestnuts from Around the World, MAA, 2001; 
               see p. 163.
%D A007376 M. Kraitchik, Mathematical Recreations. Dover, NY, 2nd ed., 1953, p. 
               49.
%D A007376 48th Putnam Competition, Problem A2, Math. Mag., 61 (1988), 131-134.
%D A007376 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%H A007376 Robert G. Wilson v, <a href="b007376.txt">Table of n, a(n) for n=1..100000</
               a>
%p A007376 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
%t A007376 Flatten[IntegerDigits/@Range[57]] (* Or *)
%t A007376 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}]
%Y A007376 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.
%Y A007376 Cf. A054632, A023103.
%Y A007376 For "decimations" see A127050 A127353 A127414 A127508 A127584 A127734 
               A127794 A127950 A128178 A128211 A128359 A128423 A128475 A128881.
%Y A007376 Sequence in context: A084044 A048379 A033307 this_sequence A001073 A076313 
               A055017
%Y A007376 Adjacent sequences: A007373 A007374 A007375 this_sequence A007377 A007378 
               A007379
%K A007376 base,easy,nice,nonn
%O A007376 1,2
%A A007376 N. J. A. Sloane (njas(AT)research.att.com), Robert G. Wilson v (rgwv(AT)rgwv.com)

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