A007091 -id:A007091 - cp's OEIS frontend

A014263 Numbers that contain even digits only.

0, 2, 4, 6, 8, 20, 22, 24, 26, 28, 40, 42, 44, 46, 48, 60, 62, 64, 66, 68, 80, 82, 84, 86, 88, 200, 202, 204, 206, 208, 220, 222, 224, 226, 228, 240, 242, 244, 246, 248, 260, 262, 264, 266, 268, 280, 282, 284, 286, 288, 400, 402, 404, 406, 408, 420, 422, 424

Offset: 1

N. J. A. Sloane

The set of real numbers between 0 and 1 that contain no odd digits in their decimal expansion has Hausdorff dimension log 5 / log 10.
Integers written in base 5 and then doubled (in base 10). - Franklin T. Adams-Watters, Mar 15 2006
The carryless mod 10 "even" numbers (cf. A004529) sorted and duplicates removed. - N. J. A. Sloane, Aug 03 2010.
Complement of A007957; A196564(a(n)) = 0; A103181(a(n)) = 0. - Reinhard Zumkeller, Oct 04 2011
If n-1 is represented as a base-5 number (see A007091) according to n-1 = d(m)d(m-1)…d(3)d(2)d(1)d(0) then a(n)= Sum_{j=0..m} c(d(j))*10^j, where c(k)=0,2,4,6,8 for k=0..4. - Hieronymus Fischer, Jun 03 2012

			a(1000) = 24888.
a(10^4) = 60888.
a(10^5) = 22288888.
a(10^6) = 446888888.

K. J. Falconer, The Geometry of Fractal Sets, Cambridge, 1985; p. 19.

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Index entries for 10-automatic sequences.
Index entries for sequences related to carryless arithmetic

Subsequence of A059708.

Cf. A061810, A061811, A007091, A014261, A046034, A052382, A084544, A089581, A084984, A017042, A001743, A202267, A202268, A194182, A196563.

a014263 n = a014263_list !! (n-1)
a014263_list = filter (all (`elem` "02468") . show) [0,2..]
-- Reinhard Zumkeller, Jul 05 2011

[n: n in [0..424] | Set(Intseq(n)) subset [0..8 by 2]];  // Bruno Berselli, Jul 19 2011

a:= proc(m) local L,i;
  L:= convert(m-1,base,5);
  2*add(L[i]*10^(i-1),i=1..nops(L))
end proc:
seq(a(i),i=1..100); # Robert Israel, Apr 07 2016

Select[Range[450], And@@EvenQ[IntegerDigits[#]]&] (* Harvey P. Dale, Jan 30 2011 *)
FromDigits/@Tuples[{0,2,4,6,8},3] (* Harvey P. Dale, Jul 07 2025 *)

a(n) = 2*fromdigits(digits(n-1, 5), 10); \\ Michel Marcus, Nov 04 2022

is(n)=#setminus(Set(digits(n)), [0,2,4,6,8])==0 \\ Charles R Greathouse IV, Mar 03 2025

from sympy.ntheory.digits import digits
def a(n): return int(''.join(str(2*d) for d in digits(n, 5)[1:]))
print([a(n) for n in range(58)]) # Michael S. Branicky, Jan 13 2022

from itertools import count, islice, product
def agen(): # generator of terms
    yield 0
    for d in count(1):
        for first in "2468":
            for rest in product("02468", repeat=d-1):
                yield int(first + "".join(rest))
print(list(islice(agen(), 58))) # Michael S. Branicky, Jan 13 2022

A045888(a(n)) = 0. - Reinhard Zumkeller, Aug 25 2009
a(n) = A179082(n) for n <= 25. - Reinhard Zumkeller, Jun 28 2010
From Hieronymus Fischer, Jun 06 2012: (Start)
a(n) = ((2*b_m(n)) mod 8 + 2)*10^m + Sum_{j=0..m-1} ((2*b_j(n)) mod 10)*10^j, where n>1, b_j(n) = floor((n-1-5^m)/5^j), m = floor(log_5(n-1)).
a(1*5^n+1) = 2*10^n.
a(2*5^n+1) = 4*10^n.
a(3*5^n+1) = 6*10^n.
a(4*5^n+1) = 8*10^n.
a(n) = 2*10^log_5(n-1) for n=5^k+1,
a(n) < 2*10^log_5(n-1), else.
a(n) > (8/9)*10^log_5(n-1) n>1.
a(n) = 2*A007091(n-1), iff the digits of A007091(n-1) are 0 or 1.
G.f.: g(x) = (x/(1-x))*Sum_{j>=0} 10^j*x^5^j *(1-x^5^j)* (2+4x^5^j+ 6(x^2)^5^j+ 8(x^3)^5^j)/(1-x^5^(j+1)).
Also: g(x) = 2*(x/(1-x))*Sum_{j>=0} 10^j*x^5^j * (1-4x^(3*5^j)+3x^(4*5^j))/((1-x^5^j)(1-x^5^(j+1))).
Also: g(x) = 2*(x/(1-x))*(h_(5,1)(x) + h_(5,2)(x) + h_(5,3)(x) + h_(5,4)(x) - 4*h_(5,5)(x)), where h_(5,k)(x) = Sum_{j>=0} 10^j*(x^5^j)^k/(1-(x^5^j)^5). (End)
a(5*n+i-4) = 10*a(n) + 2*i for n >= 1, i=0..4. - Robert Israel, Apr 07 2016
Sum_{n>=2} 1/a(n) = A194182. - Bernard Schott, Jan 13 2022

Examples and crossrefs added by Hieronymus Fischer, Jun 06 2012

A002278 a(n) = 4*(10^n - 1)/9.

Original entry on oeis.org

0, 4, 44, 444, 4444, 44444, 444444, 4444444, 44444444, 444444444, 4444444444, 44444444444, 444444444444, 4444444444444, 44444444444444, 444444444444444, 4444444444444444, 44444444444444444, 444444444444444444, 4444444444444444444, 44444444444444444444, 444444444444444444444

Offset: 0

N. J. A. Sloane

Ivan Panchenko, Table of n, a(n) for n = 0..200
Index entries for linear recurrences with constant coefficients, signature (11,-10).

Cf. A002275, A002276, A002277, A002279, A002280, A002281, A002282, A002283, A075415, A178632.

Cf. A007091, A010785, A017209, A024049.

LinearRecurrence[{11, -10}, {0, 4}, 20] (* Robert G. Wilson v, Jul 06 2013 *)

a(n)=4*(10^n-1)/9 \\ Charles R Greathouse IV, Sep 24 2015

a(n) = A075415(n)/A002283(n). - Reinhard Zumkeller, May 31 2010
From Vincenzo Librandi, Jul 22 2010: (Start)
a(n) = a(n-1) + 4*10^(n-1) with a(0)=0;
a(n) = 11*a(n-1) - 10*a(n-2) with a(0)=0, a(1)=4. (End)
G.f.: 4*x/((1 - x)*(1 - 10*x)). - Ilya Gutkovskiy, Feb 24 2017
E.g.f.: 4*exp(x)*(exp(9*x) - 1)/9. - Stefano Spezia, Sep 13 2023
a(n) = A007091(A024049(n)). - Michel Marcus, Jun 16 2024
From Elmo R. Oliveira, Jul 19 2025: (Start)
a(n) = 4*A002275(n).
a(n) = A010785(A017209(n-1)) for n >= 1. (End)

A001744 Numbers n such that every digit contains a loop (version 2).

Original entry on oeis.org

0, 4, 6, 8, 9, 40, 44, 46, 48, 49, 60, 64, 66, 68, 69, 80, 84, 86, 88, 89, 90, 94, 96, 98, 99, 400, 404, 406, 408, 409, 440, 444, 446, 448, 449, 460, 464, 466, 468, 469, 480, 484, 486, 488, 489, 490, 494, 496, 498, 499, 600, 604, 606, 608, 609, 640, 644, 646

Offset: 1

N. J. A. Sloane

See A001743 for the other version.

If n-1 is represented as a base-5 number (see A007091) according to n-1 = d(m)d(m-1)...d(3)d(2)d(1)d(0) then a(n)= Sum_{j=0..m} c(d(j))*10^j, where c(k)=0,4,6,8,9 for k=0..4. - Hieronymus Fischer, May 30 2012

			a(1000) = 46999.
a(10^4) = 809999.
a(10^5) = 44499999.
a(10^6) = 668999999.

Hieronymus Fischer, Table of n, a(n) for n = 1..10000
Index entries for 10-automatic sequences.

Cf. A061371, A029581, A007091, A046034, A084544, A084984, A017042, A001743, A014261, A014263, A202267, A202268.

FromDigits/@Tuples[{0,4,6,8,9},3] (* Harvey P. Dale, Aug 16 2018 *)

is(n) = #setintersect(vecsort(digits(n), , 8), [1, 2, 3, 5, 7])==0 \\ Felix Fröhlich, Sep 09 2019

From Hieronymus Fischer, May 30 2012: (Start)
a(n) = ((2*b_m(n)) mod 8 + 4 + floor(b_m(n)/4) - floor((b_m(n)+1)/4))*10^m + sum_{j=0..m-1} ((2*b_j(n))) mod 10 + 2*floor((b_j(n)+4)/5) - floor((b_j(n)+1)/5) -floor(b_j(n)/5)))*10^j, where n>1, b_j(n)) = floor((n-1-5^m)/5^j), m = floor(log_5(n-1)).
a(1*5^n+1) = 4*10^n.
a(2*5^n+1) = 6*10^n.
a(3*5^n+1) = 8*10^n.
a(4*5^n+1) = 9*10^n.
a(n) = 4*10^log_5(n-1) for n=5^k+1,
a(n) < 4*10^log_5(n-1), otherwise.
a(n) > 10^log_5(n-1) n>1.
a(n) = 4*A007091(n-1), iff the digits of A007091(n-1) are 0 or 1.
G.f.: g(x) = (x/(1-x))*sum_{j>=0} 10^j*x^5^j*(1-x^5^j)*(4 + 6x^5^j + 8(x^2)^5^j + 9(x^3)^5^j)/(1-x^5^(j+1)).
Also: g(x) = (x/(1-x))*(4*h_(5,1)(x) + 2*h_(5,2)(x) + 2*h_(5,3)(x) + h_(5,4)(x) - 9*h_(5,5)(x)), where h_(5,k)(x) = sum_{j>=0} 10^j*(x^5^j)^k/(1-(x^5^j)^5). (End)

Ambiguous comment deleted by Zak Seidov, May 25 2010

Examples added by Hieronymus Fischer, May 30 2012

A031235 Triangle T(n,k): write n in base 5, reverse order of digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 0, 1, 1, 1, 2, 1, 3, 1, 4, 1, 0, 2, 1, 2, 2, 2, 3, 2, 4, 2, 0, 3, 1, 3, 2, 3, 3, 3, 4, 3, 0, 4, 1, 4, 2, 4, 3, 4, 4, 4, 0, 0, 1, 1, 0, 1, 2, 0, 1, 3, 0, 1, 4, 0, 1, 0, 1, 1, 1, 1, 1, 2, 1, 1, 3, 1, 1, 4, 1, 1, 0, 2, 1, 1, 2, 1, 2, 2, 1, 3, 2, 1, 4, 2, 1, 0

Offset: 0

Clark Kimberling

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

Cf. A030308, A030341, A030386, A030567, A031007, A031045, A031087, A031298 for the base-2 to base-10 analogs.

Cf. A007091.

a031235 n k = a031235_tabf !! n !! k
a031235_row n = a031235_tabf !! n
a031235_tabf = iterate succ [0] where
   succ []     = [1]
   succ (4:ts) = 0 : succ ts
   succ (t:ts) = (t + 1) : ts
-- Reinhard Zumkeller, Sep 18 2015

Reverse[IntegerDigits[#,5]]&/@Range[0,40]//Flatten (* Harvey P. Dale, Aug 02 2016 *)

A031235(n, k=-1)=/*k<0&&error("Flattened sequence not yet implemented.")*/n\5^k%5 \\ Assuming that columns are numbered starting with k=0 as in A030308, A030341, ... - M. F. Hasler, Jul 21 2013

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

A029988 Numbers k such that k^2 is palindromic in base 5.

Original entry on oeis.org

0, 1, 2, 6, 26, 31, 66, 126, 156, 626, 651, 756, 804, 3126, 3276, 3756, 9054, 15626, 15751, 16276, 18434, 18756, 32578, 34162, 46704, 78126, 78876, 81276, 93756, 390626, 391251, 393876, 406276, 468756, 487981, 1166454, 1953126, 1956876

Offset: 1

Patrick De Geest

Patrick De Geest, Palindromic Squares in bases 2 to 17
G. J. Simmons, On palindromic squares of non-palindromic numbers, J. Rec. Math., 5 (No. 1, 1972), 11-19. [Annotated scanned copy]

Cf. A002778, A003166, A007091, A263611, A263612, A029989.

pal5Q[n_]:=Module[{idn5=IntegerDigits[n^2,5]},idn5==Reverse[idn5]]; Select[ Range[ 0,2*10^6],pal5Q] (* Harvey P. Dale, Feb 02 2023 *)

A073786 Numbers in base -5.

Original entry on oeis.org

0, 1, 2, 3, 4, 140, 141, 142, 143, 144, 130, 131, 132, 133, 134, 120, 121, 122, 123, 124, 110, 111, 112, 113, 114, 100, 101, 102, 103, 104, 240, 241, 242, 243, 244, 230, 231, 232, 233, 234, 220, 221, 222, 223, 224, 210, 211, 212, 213, 214, 200, 201, 202, 203

Offset: 0

Robert G. Wilson v, Aug 11 2002

D. E. Knuth, The Art of Computer Programming. Addison-Wesley, Reading, MA, 1969, Vol. 2, p. 189.

Chai Wah Wu, Table of n, a(n) for n = 0..10000
Eric Weisstein's World of Mathematics, Negabinary
Prepared and presented by Matthew Szudzik of Wolfram Research, A Mathematica programming contest

Cf. A007091, A039724, A073785, A007608, A073787, A073788, A073789, A073790 & A039723.

ToNegaBases[i_Integer, b_Integer] := FromDigits[ Rest[ Reverse[ Mod[ NestWhileList[(#1 - Mod[ #1, b])/-b &, i, #1 != 0 &], b]]]]; Table[ ToNegaBases[n, 5], {n, 0, 55}]

def A073786(n):
    s, q = '', n
    while q >= 5 or q < 0:
        q, r = divmod(q, -5)
        if r < 0:
            q += 1
            r += 5
        s += str(r)
    return int(str(q)+s[::-1]) # Chai Wah Wu, Apr 09 2016

A102491 Numbers whose base-20 representation can be written with decimal digits.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 80, 81, 82, 83, 84, 85, 86, 87, 88, 89, 100, 101, 102, 103, 104, 105, 106, 107, 108, 109, 120, 121, 122, 123, 124, 125, 126

Offset: 1

Reinhard Zumkeller, Jan 12 2005

a(n) = A118761(n) for n<=50. - Reinhard Zumkeller, May 01 2006

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Vigesimal
Wikipedia, Vigesimal

Complement of A102492; Cf. A102487, A102489, A102493. Cf. A037454, A037462, A007091.

import Data.List (unfoldr)
a102491 n = a102491_list !! (n-1)
a102491_list = filter (all (<= 9) . unfoldr
   (\x -> if x == 0 then Nothing else Just $ swap $ divMod x 20)) [0..]
-- Reinhard Zumkeller, Jun 27 2013

seq(n + (1/2)*add(20^k*floor(n/10^k), k = 1..floor(ln(n)/ln(10))), n = 1..100); # Peter Bala, Dec 01 2016

Select[Range@ 126, Total@ Take[Most@ DigitCount[#, 20], -10] == 0 &] (* Michael De Vlieger, Apr 09 2016 *)

isok(n) = (n==0) || ((d=digits(n, 20)) && (vecmax(d) < 10)); \\ Michel Marcus, Apr 09 2016

a(n) = fromdigits(digits(n-1),20) \\ Ruud H.G. van Tol, Dec 08 2022

A102491_list = [int(str(x), 20) for x in range(10**6)] # Chai Wah Wu, Apr 09 2016

From Peter Bala, Dec 01 2016: (Start)
If n = Sum_{i = 0..m} d(i)*10^i is the decimal expansion of n then a(n+1) = Sum_{i = 0..m} d(i)*20^i.
a(n+1) = n + 1/2*Sum_{k >= 1} 20^k*floor(n/10^k). Cf. A037454, A037462 and A007091.
a(1) = 0; a(n+1) = 20*a(n/10+1) if n == 0 (mod 10) else a(n+1) = a(n) + 1. (End)
G.f. g(x) satisfies g(x) = 20*Sum_{1<=k<=9} x^k*g(x^10)/x^9 + Sum_{1<=k<=9} k*x^(k+1)/(1-x^10). - Robert Israel, Dec 01 2016

A037453 Positive numbers whose base-5 representation contains no 3 or 4.

Original entry on oeis.org

1, 2, 5, 6, 7, 10, 11, 12, 25, 26, 27, 30, 31, 32, 35, 36, 37, 50, 51, 52, 55, 56, 57, 60, 61, 62, 125, 126, 127, 130, 131, 132, 135, 136, 137, 150, 151, 152, 155, 156, 157, 160, 161, 162, 175, 176, 177, 180, 181, 182, 185, 186, 187

Offset: 1

Clark Kimberling

5 divides neither C(2s-1,s) = A001700(s) (nor C(2s,s) = A000984(s), central column of Pascal's Triangle) if and only if s is one of the terms in this sequence.
k such that binomial(2k,k) != 0 (mod 10). - Benoit Cloitre, Aug 18 2002
Let us recall the plan of Apery's irrationality proof. Consider the recurrence (n+1)^3 * u_(n+1) = (34n^3 + 51n^2 + 27n + 5)u_n - n^3 * u_(n-1). The solution with starting values u_0 = 1; u_1 = 5 has the peculiar property that it has integral terms, despite the fact that at every recursion step we divide by (n+1)^3. The n-th term is given by f(n) = Sum_{i=0..n} binomial(n+i,i)^2 * binomial(n,i)^2 = A005259(n) (see Beukers link) and m such that f(m) mod 5 <> 0 equals 2*a(m). - Mohammed Bouayoun (bouyao(AT)wanadoo.fr), Mar 08 2004
Numbers k such that A208279(k) <> 0. A073095 is a subsequence. - Chai Wah Wu, Dec 08 2023

			From _David A. Corneth_, Dec 23 2023: (Start)
27_10 = 102_5 is a term since its base-5 representation contains no 3 and no 4.
28_10 = 103_5 is not a term since its base-5 representation contains a 3.
(End)

Clark Kimberling, Table of n, a(n) for n = 1..1000
Frits Beukers Consequences of Apery's work on zeta(3), Rencontres Arithmétiques de Caen, zeta(3) irrationnel: les retombées, 1995.
Barry Brent, On the Constant Terms of Certain Laurent Series, Preprints (2023) 2023061164.
W. Shur, The last digit of C(2*n,n) and sigma C(n,i)*C(2*n-2*i,n-i), The Electronic Journal of Combinatorics, R16, Volume 4, Issue 2 (1997).

Cf. A050607, A005836, A007091.

Cf. A000984, A073095, A208279.

function a(n)
    m, r, b = n, 0, 1
    while m > 0
        m, q = divrem(m, 3)
        r += b * q
        b *= 5
    end
r end; [a(n) for n in 1:53] |> println # Peter Luschny, Jan 03 2021

a:= proc(t) option remember; 5*procname(floor(t/3))+ (t mod 3) end proc:
a(0):= 0:
seq(a(n),n=1..100); # Robert Israel, Sep 02 2014

Table[FromDigits[IntegerDigits[k,3],5], {k,60}] (* T. D. Noe, Apr 18 2007 *)
Rest[FromDigits[#,5]&/@Tuples[{0,1,2},4]] (* Harvey P. Dale, Aug 31 2016 *)
Select[Range[187], !Divisible[Binomial[2#, #], 10]&] (* Stefano Spezia, Dec 09 2023 *)

f(n)=sum(i=0,n,binomial(n+i,i)^2*binomial(n,i)^2); for (i=1,1000,if(Mod(f(i),5)<>0,print1(i/2,",")))

isok(k) = binomial(2*k, k) % 10; \\ Michel Marcus, Dec 08 2023

is(n) = my(s = Set(digits(n, 5))); s[#s] < 3 \\ David A. Corneth, Dec 23 2023

a(n) = fromdigits(digits(n, 3), 5) \\ David A. Corneth, Dec 23 2023

from itertools import count, islice
from sympy.ntheory.factor_ import digits
def A037453_gen(startvalue=1): # generator of terms >= startvalue
    if startvalue <= 0: yield 0
    yield from filter(lambda n: all(x<3 for x in digits(n, 5)[1:]), count(max(startvalue, 1)))
A037453_list = list(islice(A037453_gen(), 30)) # Chai Wah Wu, Dec 08 2023

from gmpy2 import digits
def A037453(n): return int(digits(n,3),5) # Chai Wah Wu, Aug 10 2025

a(3n)=5a(n), a(3n+1)=5a(n)+1, a(3n+2)=5a(n)+2, where by definition a(0)=0. - Emeric Deutsch, Mar 23 2004

G.f. satisfies g(x) = 5*(1+x+x^2)*g(x^3) + (x + 2*x^2)/(1-x^3). - Robert Israel, Sep 02 2014

Better definition from T. D. Noe, Apr 18 2007

A073792 Replace 5^k with (-5)^k in base 5 expansion of n.

Original entry on oeis.org

0, 1, 2, 3, 4, -5, -4, -3, -2, -1, -10, -9, -8, -7, -6, -15, -14, -13, -12, -11, -20, -19, -18, -17, -16, 25, 26, 27, 28, 29, 20, 21, 22, 23, 24, 15, 16, 17, 18, 19, 10, 11, 12, 13, 14, 5, 6, 7, 8, 9, 50, 51, 52, 53, 54, 45, 46, 47, 48, 49, 40, 41, 42, 43, 44, 35, 36, 37, 38, 39, 30, 31, 32, 33, 34

Offset: 0

Robert G. Wilson v, Aug 12 2002

Base 5 representation for n converted from base -5 to base 10.

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. A007091, A073786, A053985, A065369, A073791, 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, 5]], {n, 0, 80}]; b = {}; Do[b = Append[b, f[a[[n]], 5]], {n, 1, 80}]; b

a(5*k+m) = -5*a(k)+m for 0 <= m < 5. - Chai Wah Wu, Jan 16 2020

A346689 Replace 5^k with (-1)^k in base-5 expansion of n.

Original entry on oeis.org

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

Offset: 0

Ilya Gutkovskiy, Jul 29 2021

If n has base-5 expansion abc..xyz with least significant digit z, a(n) = z - y + x - w + ...

			48 = 143_5, 3 - 4 + 1 = 0, so a(48) = 0.

Cf. A007091, A053824, A055017, A065359, A065368, A346688, A346690, A346691.

nmax = 104; A[] = 0; Do[A[x] = x (1 + 2 x + 3 x^2 + 4 x^3)/(1 - x^5) - (1 + x + x^2 + x^3 + x^4) A[x^5] + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x]
Table[n + 6 Sum[(-1)^k Floor[n/5^k], {k, 1, Floor[Log[5, n]]}], {n, 0, 104}]

from sympy.ntheory.digits import digits
def a(n):
    return sum(bi*(-1)**k for k, bi in enumerate(digits(n, 5)[1:][::-1]))
print([a(n) for n in range(105)]) # Michael S. Branicky, Jul 29 2021

G.f. A(x) satisfies: A(x) = x * (1 + 2*x + 3*x^2 + 4*x^3) / (1 - x^5) - (1 + x + x^2 + x^3 + x^4) * A(x^5).

a(n) = n + 6 * Sum_{k>=1} (-1)^k * floor(n/5^k).

cp's OEIS Frontend

A014263 Numbers that contain even digits only.

Views

Author

Keywords

Comments

Examples

References

Links

Crossrefs

Programs

Haskell

Magma

Maple

Mathematica

PARI

PARI

Python

Python

Formula

Extensions

A002278 a(n) = 4*(10^n - 1)/9.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A001744 Numbers n such that every digit contains a loop (version 2).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

PARI

Formula

Extensions

A031235 Triangle T(n,k): write n in base 5, reverse order of digits.

Views

Author

Keywords

Links

Crossrefs

Programs

Haskell

Mathematica

PARI

Extensions

A029988 Numbers k such that k^2 is palindromic in base 5.

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

A073786 Numbers in base -5.

Views

Author

Keywords

References

Links

Crossrefs

Programs

Mathematica

Python

A102491 Numbers whose base-20 representation can be written with decimal digits.

Views

Author

Keywords

Comments

Links

Crossrefs