A003137 Write n in base 3 and juxtapose.

1, 2, 1, 0, 1, 1, 1, 2, 2, 0, 2, 1, 2, 2, 1, 0, 0, 1, 0, 1, 1, 0, 2, 1, 1, 0, 1, 1, 1, 1, 1, 2, 1, 2, 0, 1, 2, 1, 1, 2, 2, 2, 0, 0, 2, 0, 1, 2, 0, 2, 2, 1, 0, 2, 1, 1, 2, 1, 2, 2, 2, 0, 2, 2, 1, 2, 2, 2, 1, 0, 0, 0, 1, 0, 0, 1, 1, 0, 0, 2, 1, 0, 1, 0, 1, 0, 1, 1, 1, 0, 1, 2, 1, 0, 2, 0, 1, 0, 2, 1, 1, 0, 2, 2, 1

Offset: 1

Author

N. J. A. Sloane

Keywords

• nonn
• base
• cons
• easy
• tabf

Comments

An irregular table in which the n-th row lists the base-3 digits of n, see A007089. - Jason Kimberley, Dec 07 2012

The base-3 Champernowne constant (A077771): it is normal in base 3. - Jason Kimberley, Dec 07 2012

Examples

			1,
2,
1,0,
1,1,
1,2,
2,0,
2,1,
2,2,
1,0,0,
1,0,1,.... _R. J. Mathar_, Aug 16 2021
		

References

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

Links

• Reinhard Zumkeller, Rows n = 1..1000 of triangle, flattened
• Eric Weisstein's World of Mathematics, Ternary.
• Wikipedia, Ternary numeral system

Crossrefs

Tables in which the n-th row lists the base b digits of n: A030190 and A030302 (b=2), this sequence and A054635 (b=3), A030373 (b=4), A031219 (b=5), A030548 (b=6), A030998 (b=7), A031035 and A054634 (b=8), A031076 (b=9), A007376 and A033307 (b=10). - Jason Kimberley, Dec 06 2012

Cf. A081604 (row lengths), A053735 (row sums), A030341 (rows reversed), A077771, A007089.

Programs

Haskell

a003137 n k = a003137_tabf !! (n-1) !! k
a003137_row n = a003137_tabf !! (n-1)
a003137_tabf = map reverse $ tail a030341_tabf
a003137_list = concat a003137_tabf
-- Reinhard Zumkeller, Feb 21 2013

Magma

&cat[Reverse(IntegerToSequence(n,3)):n in[1..31]]; // Jason Kimberley, Dec 07 2012

Mathematica

Flatten@ IntegerDigits[ Range@ 40, 3] (* 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[ a[#, 3] &, 105] (* Robert G. Wilson v, Jul 01 2014 *)

Python

from itertools import count, islice
from sympy.ntheory.factor_ import digits
def A003137_gen(): return (d for m in count(1) for d in digits(m,3)[1:])
A003137_list = list(islice(A003137_gen(),30)) # Chai Wah Wu, Jan 07 2022

Extensions

More terms from Larry Reeves (larryr(AT)acm.org), Sep 25 2000