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A007376 The almost-natural numbers: write n in base 10 and juxtapose digits.
(Formerly M0469)
97
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; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also called the Barbier infinite word.

This is an example of a non-morphic sequence.

a(n) = A162711(n,1); A136414(n) = 10*a(n) + a(n+1). [From Reinhard Zumkeller, Jul 11 2009]

a(A031287(n))=0, a(A031288(n))=1, a(A031289(n))=2, a(A031290(n))=3, a(A031291(n))=4, a(A031292(n))=5, a(A031293(n))=6, a(A031294(n))=7, a(A031295(n))=8, a(A031296(n))=9. [Reinhard Zumkeller, Jul 28 2011]

May be regarded as an irregular table in which the n-th row lists the digits of n. - Jason Kimberley, Dec 07 2012

REFERENCES

J.-P. Allouche and J. Shallit, Automatic Sequences, Cambridge Univ. Press, 2003, pp. 114, 336.

R. Honsberger, Mathematical Chestnuts from Around the World, MAA, 2001; see p. 163.

M. Kraitchik, Mathematical Recreations. Dover, NY, 2nd ed., 1953, p. 49.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Robert G. Wilson v, Table of n, a(n) for n = 1..100000

Putnam Competition No. 48, Problem A2, Math. Mag., 61 (1988), 131-134.

MAPLE

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, Jul 27 2006

MATHEMATICA

Flatten[ IntegerDigits /@ Range@ 57] (* Or *)

almostNatural[n_, b_] := Block[{m = 0, d = n, i = 1, l, p}, While[m <= d, l = m; m = (b - 1) i*b^(i - 1) + l; i++]; i--; p = Mod[d - l, i]; q = Floor[(d - l)/i] + b^(i - 1); If[p != 0, IntegerDigits[q, b][[p]], Mod[q - 1, b]]]; Array[ almostNatural[#, 10] &, 105] (* updated June 29 2014 *)

PROG

(Haskell)

a007376 n = a007376_list !! (n-1)

a007376_list = concatMap (map (read . return) . show) [1..] :: [Int]

-- Reinhard Zumkeller, Nov 11 2013, Dec 17 2011, Mar 28 2011

(PARI) for(n=1, 90, v=digits(n); for(i=1, #v, print1(v[i]", "))) \\ Charles R Greathouse IV, Nov 20 2012

(MAGMA) &cat[Reverse(IntegerToSequence(n)):n in[1..31]]; // Jason Kimberley, Dec 07 2012

CROSSREFS

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 (partial sums), A023103.

For "decimations" see A127050 A127353 A127414 A127508 A127584 A127734 A127794 A127950 A128178 A128211 A128359 A128423 A128475 A128881.

Cf. A193428.

Tables in which the n-th row lists the base b digits of n: A030190 and A030302 (b=2), A003137 and A054635 (b=3), A030373 (b=4), A031219 (b=5), A030548 (b=6), A030998 (b=7), A031035 and A054634 (b=8), A031076 (b=9), this sequence and A033307 (b=10). - Jason Kimberley, Dec 06 2012

Row lengths in A055642.

Cf. A000027.

Sequence in context: A169930 A179295 A033307 * A189823 A001073 A241494

Adjacent sequences:  A007373 A007374 A007375 * A007377 A007378 A007379

KEYWORD

base,easy,nice,nonn,tabf

AUTHOR

N. J. A. Sloane, Robert G. Wilson v

STATUS

approved

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Last modified November 23 19:50 EST 2014. Contains 249865 sequences.