A030341 -id:A030341 - cp's OEIS frontend

A023717 Numbers with no 3's in base-4 expansion.

0, 1, 2, 4, 5, 6, 8, 9, 10, 16, 17, 18, 20, 21, 22, 24, 25, 26, 32, 33, 34, 36, 37, 38, 40, 41, 42, 64, 65, 66, 68, 69, 70, 72, 73, 74, 80, 81, 82, 84, 85, 86, 88, 89, 90, 96, 97, 98, 100, 101, 102, 104, 105, 106, 128, 129, 130, 132, 133, 134, 136, 137, 138

Offset: 0

Olivier Gérard

A032925 is the intersection of this sequence and A023705; cf. A179888. - Reinhard Zumkeller, Jul 31 2010

Fixed point of the morphism: 0-> 0,1,2; 1-> 4,5,6; 2-> 8,9,10; ...; n-> 4n,4n+1,4n+2. - Philippe Deléham, Oct 22 2011

Reinhard Zumkeller, Table of n, a(n) for n = 0..10000

Cf. A032925, A023705, A179888.

uint32_t a_next(uint32_t a_n) {
    uint32_t t = ((a_n ^ 0xaaaaaaaa) | 0x55555555) >> 1;
    return (a_n - t) & t;
} // Falk Hüffner, Jan 22 2022

a023717 n = a023717_list !! (n-1)
a023717_list = filter f [0..] where
   f x = x < 3 || (q < 3 && f x') where (x', q) = divMod x 4
-- Reinhard Zumkeller, Apr 18 2015

function a(n)
    m, r, b = n, 0, 1
    while m > 0
        m, q = divrem(m, 3)
        r += b * q
        b *= 4
    end
r end; [a(n) for n in 0:58] |> println # Peter Luschny, Jan 03 2021

Select[ Range[ 0, 140 ], (Count[ IntegerDigits[ #, 4 ], 3 ]==0)& ]

a(n)=if(n<1,0,if(n%3,a(n-1)+1,4*a(n/3)))

a(n)=if(n<1,0,4*a(floor(n/3))+n-3*floor(n/3))

from gmpy2 import digits
def A023717(n): return int(digits(n,3),4) # Chai Wah Wu, May 06 2025

a(n) = Sum_{i=0..m} d(i)*4^i, where Sum_{i=0..m} d(i)*3^i is the base-3 representation of n. - Clark Kimberling
a(3n) = 4*a(n); a(3n+1) = 4*a(n)+1; a(3n+2) = 4*a(n)+2; a(n) = 4*a(floor(n/3)) + n - 3*floor(n/3). - Benoit Cloitre, Apr 27 2003
a(n) = Sum_{k>=0} A030341(n,k)*4^k. - Philippe Deléham, Oct 22 2011

A031087 Triangle T(n,k): write n in base 9, reverse order of digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 8, 1, 0, 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7, 2, 8, 2, 0, 3, 1, 3, 2, 3, 3, 3, 4, 3, 5, 3, 6, 3, 7, 3, 8, 3, 0, 4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6, 4, 7, 4, 8, 4, 0, 5, 1, 5, 2, 5, 3, 5, 4, 5

Offset: 0

Clark Kimberling

Reinhard Zumkeller, Rows n = 0..1000 of triangle, flattened

Cf. A030308, A030341, A030386, A031235, A030567, A031007, A031045, A031298 for the base-2 to base-10 analogs.

Cf. A031076, A007095.

a031087 n k = a031087_row n !! (k-1)
a031087_row n | n < 9     = [n]
              | otherwise = m : a031087_row n' where (n',m) = divMod n 9
a031087_tabf = map a031087_row [0..]
-- Reinhard Zumkeller, Jul 07 2015

A031087(n, k=-1)=/*k<0&&error("Flattened sequence not yet implemented.")*/n\9^k%9 \\ Assuming that columns are numbered starting with k=0 as in A030308, A030567 and others. - M. F. Hasler, Jul 21 2013

Initial 0 and better name by Philippe Deléham, Oct 20 2011

A054635 Champernowne sequence: write n in base 3 and juxtapose.

Original entry on oeis.org

0, 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

Offset: 0

N. J. A. Sloane, Apr 16 2000

Essentially the same as A003137. - R. J. Mathar, Aug 29 2009
An irregular table in which the n-th row lists the base-3 digits of n. - Jason Kimberley, Dec 07 2012
The base-3 Champernowne constant (A077771): it is normal in base 3. - Jason Kimberley, Dec 07 2012

Reinhard Zumkeller, Rows n = 0..1000 of triangle, flattened
Eric Weisstein's World of Mathematics, Ternary Champernowne Constant
Wikipedia, Ternary numeral system

Cf. A054637 (partial sums).
Cf. A081604 (row lengths), A053735 (row sums), A030341 (rows reversed), A007089, A077771.
Table in which the n-th row lists the base b digits of n: A030190 and A030302 (b=2), A003137 and this sequence (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

a054635 n k = a054635_tabf !! n !! k
a054635_row n = a054635_tabf !! n
a054635_tabf = map reverse a030341_tabf
a054635_list = concat a054635_tabf
-- Reinhard Zumkeller, Feb 21 2013

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

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[#, 3] &, 105, 0] (* Robert G. Wilson v, Jun 29 2014 *)
First[RealDigits[ChampernowneNumber[3], 3, 100, 0]] (* Paolo Xausa, Jun 19 2024 *)

from sympy.ntheory.digits import digits
def agen(limit):
    for n in range(limit):
        yield from digits(n, 3)[1:]
print([an for an in agen(35)]) # Michael S. Branicky, Sep 01 2021

A031045 Triangle T(n,k): write n in base 8, reverse order of digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 7, 1, 0, 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 7, 2, 0, 3, 1, 3, 2, 3, 3, 3, 4, 3, 5, 3, 6, 3, 7, 3, 0, 4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6, 4, 7, 4, 0, 5, 1, 5, 2, 5, 3, 5, 4, 5, 5, 5, 6, 5, 7, 5, 0, 6, 1

Offset: 0

Clark Kimberling

Robert Israel, Table of n, a(n) for n = 0..10003 (rows 0 to 3646, flattened)

Cf. A030308, A030341, A030386, A031235, A030567, A031007, A031087, A031298 for the base-2 to base-10 analogs.

seq(op(convert(n,base,8)),n=0..100); # Robert Israel, Jul 22 2019

Flatten[Table[Reverse[IntegerDigits[n,8]],{n,80}]] (* Harvey P. Dale, Aug 08 2011 *)

A031045(n, k=-1)=/*k<0&&error("Flattened sequence not yet implemented.");*/n\8^k%8 \\ Assuming that columns are numbered starting with k=0 as in A030308, A030341, ... Note: The operation could be done using bitwise arithmetic, bitand(n>>(3*k),7), but this is not significantly faster in PARI. - M. F. Hasler, Jul 21 2013

Initial 0 and better name by Philippe Deléham, Oct 20 2011

A065361 Rebase n from 3 to 2. Replace 3^k with 2^k in ternary expansion of n.

Original entry on oeis.org

0, 1, 2, 2, 3, 4, 4, 5, 6, 4, 5, 6, 6, 7, 8, 8, 9, 10, 8, 9, 10, 10, 11, 12, 12, 13, 14, 8, 9, 10, 10, 11, 12, 12, 13, 14, 12, 13, 14, 14, 15, 16, 16, 17, 18, 16, 17, 18, 18, 19, 20, 20, 21, 22, 16, 17, 18, 18, 19, 20, 20, 21, 22, 20, 21, 22, 22, 23, 24, 24, 25, 26, 24, 25, 26, 26, 27

Offset: 0

Marc LeBrun, Oct 31 2001

Notation: (3)[n](2).

Fixed point of the morphism 0->0,1,2; 1->2,3,4; 2->4,5,6; ...; n->2n,2n+1,2n+2. - Philippe Deléham, Oct 22 2011

			15 = 120 -> 1(4)+2(2)+0(1) = 8 = a(15).

Harry J. Smith, Table of n, a(n) for n = 0..1000

Cf. A065362, A030341.

function a(n)
    m, r, b = n, 0, 1
    while m > 0
        m, q = divrem(m, 3)
        r += b * q
        b *= 2
    end
r end; [a(n) for n in 0:76] |> println # Peter Luschny, Jan 03 2021

t = Table[FromDigits[RealDigits[n, 3], 2], {n, 0, 100}]
(* Clark Kimberling, Aug 02 2012 *)

a(n)=if(n<1,0,if(n%3,a(n-1)+1,2*a(n/3)))

a(n)=if(n<1,0,2*a(floor(n/3))+n-3*floor(n/3))

Rebase(x, b, c)= { local(d, e=0, f=1); while (x>0, d=x-b*(x\b); x\=b; e+=d*f; f*=c); return(e) } { for (n=0, 1000, write("b065361.txt", n, " ", Rebase(n, 3, 2)) ) } \\ Harry J. Smith, Oct 17 2009

a(0)=0, a(3n)=2*a(n), a(3n+1)=2*a(n)+1, a(3n+2)=2*a(n)+2. - Benoit Cloitre, Dec 21 2002
a(n) = 2*a(floor(n/3))+n-3*floor(n/3). - Benoit Cloitre, Apr 27 2003
a(n) = Sum_{k>=0} A030341(n,k)*2^k. - Philippe Deléham, Oct 22 2011

A031007 Triangle T(n,k): Write n in base 7, reverse order of digits, to get row n.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, 1, 0, 2, 1, 2, 2, 2, 3, 2, 4, 2, 5, 2, 6, 2, 0, 3, 1, 3, 2, 3, 3, 3, 4, 3, 5, 3, 6, 3, 0, 4, 1, 4, 2, 4, 3, 4, 4, 4, 5, 4, 6, 4, 0, 5, 1, 5, 2, 5, 3, 5, 4, 5, 5, 5, 6, 5, 0, 6, 1, 6, 2, 6, 3, 6, 4, 6, 5, 6, 6, 6

Offset: 0

Clark Kimberling

Cf. A030308, A030341, A030386, A031235, A030567, A031045, A031087, A031298 for the base-2 to base-10 analogs.

Flatten[Table[Reverse[IntegerDigits[n,7]],{n,0,50}]] (* Harvey P. Dale, Feb 25 2014 *)

A031007(n, k=-1)={k<0&&error("Flattened sequence not yet implemented.");n\7^k%7} \\ Assuming that columns start with k=0 as in A030308, A030341, ... TO DO: implement flattened sequence, such that A030567(n)=a(n). - M. F. Hasler, Jul 21 2013

Initial 0 and better name by Philippe Deléham, Oct 20 2011

A047240 Numbers that are congruent to {0, 1, 2} mod 6.

Original entry on oeis.org

0, 1, 2, 6, 7, 8, 12, 13, 14, 18, 19, 20, 24, 25, 26, 30, 31, 32, 36, 37, 38, 42, 43, 44, 48, 49, 50, 54, 55, 56, 60, 61, 62, 66, 67, 68, 72, 73, 74, 78, 79, 80, 84, 85, 86, 90, 91, 92, 96, 97, 98, 102, 103, 104, 108, 109, 110, 114, 115, 116, 120, 121, 122

Offset: 1

N. J. A. Sloane

Partial sums of 0,1,1,4,1,1,4,... - Paul Barry, Feb 19 2007

Numbers k such that floor(k/3) = 2*floor(k/6). - Bruno Berselli, Oct 05 2017

Vincenzo Librandi, Table of n, a(n) for n = 1..10000
Vladimir Pletser, Congruence conditions on the number of terms in sums of consecutive squared integers equal to squared integers, arXiv:1409.7969 [math.NT], 2014.
Index entries for linear recurrences with constant coefficients, signature (1,0,1,-1).

Cf. A010872, A030341, A047234, A047242.

Cf. similar sequences with formula n+i*floor(n/3) listed in A281899.

[0] cat [6*Floor(n/3) + (n mod 3): n in [1..65]]; // Vincenzo Librandi, Oct 23 2011

A047240:=n->2*n-3-cos(2*n*Pi/3)+sin(2*n*Pi/3)/sqrt(3): seq(A047240(n), n=1..100); # Wesley Ivan Hurt, Jun 14 2016
select(k -> modp(iquo(k,3), 2) = 0, [$0..122]); # Peter Luschny, Oct 05 2017

Select[Range[0, 200], Mod[#, 6] == 0 || Mod[#, 6] == 1 || Mod[#, 6] == 2 &] (* Vladimir Joseph Stephan Orlovsky, Jul 07 2011 *)
a047240[n_] := Flatten[Map[6 # + {0, 1, 2} &, Range[0, n]]]; a047240[20] (* data *) (* Hartmut F. W. Hoft, Mar 06 2017 *)

a(n)=n\3*6 + n%3 \\ Charles R Greathouse IV, Oct 07 2015

[k for k in range(123) if (k//3) % 2 == 0] # Peter Luschny, Oct 05 2017

From Paul Barry, Feb 19 2007: (Start)
G.f.: x*(1 + x + 4*x^2)/((1 - x)*(1 - x^3)).
a(n) = 2*n - 3 - cos(2*n*Pi/3) + sin(2*n*Pi/3)/sqrt(3). (End)
a(n) = n-1 + 3*floor((n-1)/3). - Philippe Deléham, Apr 21 2009
a(n) = 6*floor(n/3) + (n mod 3). - Gary Detlefs, Mar 09 2010
a(n+1) = Sum_{k>=0} A030341(n,k)*b(k) with b(0)=1 and b(k)=2*3^k for k>0. - Philippe Deléham, Oct 22 2011.
a(n) = 2*n - 2 - A010872(n-1). - Wesley Ivan Hurt, Jul 07 2013
From Wesley Ivan Hurt, Jun 14 2016: (Start)
a(n) = a(n-1) + a(n-3) - a(n-4) for n>4.
a(3*k) = 6*k-4, a(3*k-1) = 6*k-5, a(3*k-2) = 6*k-6. (End)
Sum_{n>=2} (-1)^n/a(n) = (3-sqrt(3))*Pi/18 + log(2+sqrt(3))/(2*sqrt(3)). - Amiram Eldar, Dec 14 2021
E.g.f.: 4 + exp(x)*(2*x - 3) - exp(-x/2)*(3*cos(sqrt(3)*x/2) - sqrt(3)*sin(sqrt(3)*x/2))/3. - Stefano Spezia, Jul 26 2024

Paul Barry formula adapted for offset 1 by Wesley Ivan Hurt, Jun 14 2016

A065368 Alternating sum of ternary digits in n. Replace 3^k with (-1)^k in ternary expansion of n.

Original entry on oeis.org

0, 1, 2, -1, 0, 1, -2, -1, 0, 1, 2, 3, 0, 1, 2, -1, 0, 1, 2, 3, 4, 1, 2, 3, 0, 1, 2, -1, 0, 1, -2, -1, 0, -3, -2, -1, 0, 1, 2, -1, 0, 1, -2, -1, 0, 1, 2, 3, 0, 1, 2, -1, 0, 1, -2, -1, 0, -3, -2, -1, -4, -3, -2, -1, 0, 1, -2, -1, 0, -3, -2, -1, 0, 1, 2, -1, 0, 1, -2, -1, 0, 1, 2, 3, 0, 1, 2, -1, 0, 1, 2, 3, 4, 1, 2, 3, 0, 1, 2, 3, 4, 5, 2, 3

Offset: 0

Marc LeBrun, Oct 31 2001

Notation: (3)[n](-1).

Fixed point of the morphism 0 -> 0,1,2; 1 -> -1,0,1; 2 -> -2,-1,0; ...; n -> -n,-n+1,-n+2. - Philippe Deléham, Oct 22 2011

			15 = +1(9)+2(3)+0(1) -> +1(+1)+2(-1)+0(+1) = -1 = a(15).

Cf. A030341, A053735, A065359, A065364.

from sympy.ntheory.digits import digits
def a(n):
    return sum(bi*(-1)**k for k, bi in enumerate(digits(n, 3)[1:][::-1]))
print([a(n) for n in range(104)]) # Michael S. Branicky, Jul 28 2021

from sympy.ntheory import digits
def A065368(n): return sum((0, 1, 2, -1, 0, 1, -2, -1, 0)[i] for i in digits(n,9)[1:]) # Chai Wah Wu, Jul 19 2024

a(n) = Sum_{k>=0} A030341(n,k)*(-1)^k. - Philippe Deléham, Oct 22 2011.

G.f. A(x) satisfies: A(x) = x * (1 + 2*x) / (1 - x^3) - (1 + x + x^2) * A(x^3). - Ilya Gutkovskiy, Jul 28 2021

Initial 0 added by Philippe Deléham, Oct 22 2011

A065369 Replace 3^k with (-3)^k in ternary expansion of n.

Original entry on oeis.org

0, 1, 2, -3, -2, -1, -6, -5, -4, 9, 10, 11, 6, 7, 8, 3, 4, 5, 18, 19, 20, 15, 16, 17, 12, 13, 14, -27, -26, -25, -30, -29, -28, -33, -32, -31, -18, -17, -16, -21, -20, -19, -24, -23, -22, -9, -8, -7, -12, -11, -10, -15, -14, -13, -54, -53, -52, -57, -56, -55, -60, -59, -58, -45, -44, -43, -48, -47, -46

Offset: 0

Marc LeBrun, Oct 31 2001

Base 3 representation for n (in lexicographic order) converted from base -3 to base 10.
Notation: (3)[n](-3)
Fixed point of the morphism 0-> 0,1,2 ; 1-> -3,-2,-1 ; 2-> -6,-5,-4 ; ...; n-> -3n,-3n+1,-3n+2. - Philippe Deléham, Oct 22 2011

			15 = +1(9)+2(3)+0(1) -> +1(+9)+2(-3)+0(+1) = +3 = a(15)

Rémy Sigrist, Table of n, a(n) for n = 0..19682
Dana G. Korssjoen, Biyao Li, Stefan Steinerberger, Raghavendra Tripathi, and Ruimin Zhang, Finding structure in sequences of real numbers via graph theory: a problem list, arXiv:2012.04625 [math.CO], 2020-2021.

Cf. A007089, A053985, A065367, A073785, A073791, A073792, A073793, A073794, A073795, A073796, A073835.

f[n_Integer, b_Integer] := Block[{l = IntegerDigits[n]}, Sum[l[[ -i]]*(-b)^(i - 1), {i, 1, Length[l]}]]; a = Table[ FromDigits[ IntegerDigits[n, 3]], {n, 0, 80}]; b = {}; Do[b = Append[b, f[a[[n]], 3]], {n, 1, 80}]; b

a(n) = fromdigits(digits(n, 3), -3) \\ Rémy Sigrist, Feb 06 2020

a(n) = Sum_{k>=0} A030341(n,k)*(-3)^k. - Philippe Deléham, Oct 22 2011

a(3*k+m) = -3*a(k)+m for 0 <= m < 3. - Chai Wah Wu, Jan 16 2020

A060236 If n mod 3 = 0 then a(n) = a(n/3), otherwise a(n) = n mod 3.

Original entry on oeis.org

1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 1, 1, 2, 1, 1, 2, 2, 1, 2, 2, 1, 2, 1, 1, 2, 2

Offset: 1

Henry Bottomley, Mar 21 2001

A cubefree word. Start with 1, apply the morphisms 1 -> 121, 2 -> 122, take limit. See A080846 for another version.
Ultimate modulo 3: n-th digit of terms in "Ana sequence" (see A060032 for definition).
Equals A005148(n) reduced mod 3. In "On a sequence Arising in Series for Pi" Morris Newman and Daniel Shanks conjectured that 3 never divides A005148(n) and D. Zagier proved it. - Benoit Cloitre, Jun 22 2002
Also equals A038502(n) mod 3.
Last nonzero digit in ternary representation of n. - Franklin T. Adams-Watters, Apr 01 2006
a(2*n) = length of n-th run of twos. - Reinhard Zumkeller, Mar 13 2015

			a(10)=1 since 10=3^0*10 and 10 mod 3=1;
a(72)=2 since 24=3^3*8 and 8 mod 3=2.

Reinhard Zumkeller, Table of n, a(n) for n = 1..1000
Jean Berstel and J. Karhumaki, Combinatorics on words - a tutorial, Bull. EATCS, #79 (2003), pp. 178-228.
Index entries for sequences related to final digits of numbers
Index entries for sequences that are fixed points of mappings

Cf. A026225 (indices of 1's), A026179 (indices of 2's).
Cf. A060032 (concatenate 3^n terms).
Cf. A030341, A007089.

following Franklin T. Adams-Watters's comment.
a060236 = head . dropWhile (== 0) . a030341_row
-- Reinhard Zumkeller, Mar 13 2015

[(Floor(n/3^Valuation(n, 3)) mod 3): n in [1..120]]; // G. C. Greubel, Nov 05 2024

Nest[ Flatten[ # /. {1 -> {1, 2, 1}, 2 -> {1, 2, 2}}] &, {1}, 5] (* Robert G. Wilson v, Mar 04 2005 *)
Table[Mod[n/3^IntegerExponent[n, 3], 3], {n, 1, 120}] (* Clark Kimberling, Oct 19 2016 *)
lnzd[m_]:=Module[{s=Split[m]},If[FreeQ[Last[s],0],s[[-1,1]],s[[-2,1]]]]; lnzd/@Table[IntegerDigits[n,3],{n,120}] (* Harvey P. Dale, Oct 19 2018 *)

a(n)=if(n<1, 0, n/3^valuation(n,3)%3) /* Michael Somos, Nov 10 2005 */

[n/3^valuation(n, 3)%3 for n in range(1,121)] # G. C. Greubel, Nov 05 2024

a(3*n) = a(n), a(3*n + 1) = 1, a(3*n + 2) = 2. - Michael Somos, Jul 29 2009

a(n) = 1 + A080846(n). - Joerg Arndt, Jan 21 2013

cp's OEIS Frontend

A023717 Numbers with no 3's in base-4 expansion.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

C

Haskell

Julia

Mathematica

PARI

PARI

Python

Formula

A031087 Triangle T(n,k): write n in base 9, reverse order of digits.

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

PARI

Extensions

A054635 Champernowne sequence: write n in base 3 and juxtapose.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Haskell

Magma

Mathematica

Python

A031045 Triangle T(n,k): write n in base 8, reverse order of digits.

Views

Author

Keywords

Links

Crossrefs

Programs

Maple

Mathematica

PARI

Extensions

A065361 Rebase n from 3 to 2. Replace 3^k with 2^k in ternary expansion of n.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Julia

Mathematica

PARI

PARI

PARI

Formula

A031007 Triangle T(n,k): Write n in base 7, reverse order of digits, to get row n.

Views

Author

Keywords

Crossrefs

Programs

Mathematica

PARI

Extensions

A047240 Numbers that are congruent to {0, 1, 2} mod 6.

Views

Author

Keywords

Comments

Links