A010876 -id:A010876 - cp's OEIS frontend

A130487 a(n) = Sum_{k=0..n} (k mod 9) (Partial sums of A010878).

0, 1, 3, 6, 10, 15, 21, 28, 36, 36, 37, 39, 42, 46, 51, 57, 64, 72, 72, 73, 75, 78, 82, 87, 93, 100, 108, 108, 109, 111, 114, 118, 123, 129, 136, 144, 144, 145, 147, 150, 154, 159, 165, 172, 180, 180, 181, 183, 186, 190, 195, 201, 208, 216, 216, 217, 219, 222, 226

Offset: 0

Hieronymus Fischer, May 31 2007

Let A be the Hessenberg n X n matrix defined by A[1,j]=j mod 9, A[i,i]:=1, A[i,i-1]=-1. Then, for n >= 1, a(n)=det(A). - Milan Janjic, Jan 24 2010

Shawn A. Broyles, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,1,-1).

Cf. A010872, A010873, A010874, A010875, A010876, A010877, A130481, A130482, A130483, A130484, A130485, A130486.

a:=[0,1,3,6,10,15,21,28,36,36];; for n in [11..71] do a[n]:=a[n-1]+a[n-9]-a[n-10]; od; a; # G. C. Greubel, Aug 31 2019

I:=[0,1,3,6,10,15,21,28,36,36]; [n le 10 select I[n] else Self(n-1) + Self(n-9) - Self(n-10): n in [1..71]]; // G. C. Greubel, Aug 31 2019

seq(coeff(series(x*(1-9*x^8+8*x^9)/((1-x^9)*(1-x)^3), x, n+1), x, n), n = 0 .. 70); # G. C. Greubel, Aug 31 2019

Accumulate[PadRight[{},120,Range[0,8]]] (* Harvey P. Dale, Dec 19 2018 *)
Accumulate[Mod[Range[0,100],9]] (* Harvey P. Dale, Oct 16 2021 *)

a(n) = sum(k=0, n, k % 9); \\ Michel Marcus, Apr 28 2018

def A130487_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P(x*(1-9*x^8+8*x^9)/((1-x^9)*(1-x)^3)).list()
A130487_list(70) # G. C. Greubel, Aug 31 2019

a(n) = 36*floor(n/9) + A010878(n)*(A010878(n) + 1)/2.
G.f.: (Sum_{k=1..8} k*x^k)/((1-x^9)*(1-x)).
G.f.: x*(1 - 9*x^8 + 8*x^9)/((1-x^9)*(1-x)^3).

A010883 Simple periodic sequence: repeat 1,2,3,4.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

Partial sums are given by A130482(n) + n + 1. - Hieronymus Fischer, Jun 08 2007

1234/9999 = 0.123412341234... - Eric Desbiaux, Nov 03 2008

Index entries for linear recurrences with constant coefficients, signature (0,0,0,1).

Cf. A010872, A010873, A010874, A010875, A010876, A004526, A002264, A002265, A002266.

Cf. A177037 (decimal expansion of (9+2*sqrt(39))/15). - Klaus Brockhaus, May 01 2010

PadRight[{},120,{1,2,3,4}] (* Harvey P. Dale, Aug 02 2016 *)

a(n)=(n-1)%4+1 \\ Charles R Greathouse IV, Jun 11 2015

def A010883(n): return 1 + (n & 3) # Chai Wah Wu, May 25 2022

a(n) = 1 + (n mod 4). - Paolo P. Lava, Nov 21 2006
From Hieronymus Fischer, Jun 08 2007: (Start)
a(n) = A010873(n) + 1.
Also a(n) = (1/2)*(5 - (-1)^n - 2*(-1)^((2*n - 1 + (-1)^n)/4)).
G.f.: g(x) = (4*x^3 + 3*x^2 + 2*x + 1)/(1 - x^4) = (4*x^5 - 5*x^4 + 1)/((1 - x^4)*(1-x)^2). (End)
a(n) = 5/2 - cos(Pi*n/2) - sin(Pi*n/2) - (-1)^n/2. - R. J. Mathar, Oct 08 2011

A099548 Odd part of n modulo 7.

Original entry on oeis.org

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

Offset: 1

Ralf Stephan, Oct 23 2004

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A000265, A010876.

Cf. A099544, A099545, A099546, A099547, A099549, A099550, A099551.

a[n_] := Mod[n / 2^IntegerExponent[n, 2], 7]; Array[a, 100] (* Amiram Eldar, Aug 29 2024 *)

a(n) = (n>>valuation(n, 2))%7 \\Charles R Greathouse IV, May 14 2014

a(n) = A010876(A000265(n)).

Asymptotic mean: Limit_{m->oo} (1/m) * Sum_{k=1..m} a(k) = 3. - Amiram Eldar, Aug 29 2024

A130488 a(n) = Sum_{k=0..n} (k mod 10) (Partial sums of A010879).

Original entry on oeis.org

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 45, 46, 48, 51, 55, 60, 66, 73, 81, 90, 90, 91, 93, 96, 100, 105, 111, 118, 126, 135, 135, 136, 138, 141, 145, 150, 156, 163, 171, 180, 180, 181, 183, 186, 190, 195, 201, 208, 216, 225, 225, 226, 228, 231, 235, 240, 246, 253

Offset: 0

Hieronymus Fischer, May 31 2007

nonn

Let A be the Hessenberg n X n matrix defined by A[1,j] = j mod 10, A[i,i]:=1, A[i,i-1]=-1. Then, for n >= 1, a(n)=det(A). - Milan Janjic, Jan 24 2010

Shawn A. Broyles, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,1,-1).

Cf. A010872, A010873, A010874, A010875, A010876, A010877, A010878, A130481, A130482, A130483, A130484, A130485, A130486, A130487.

a:=[0,1,3,6,10,15,21,28,36,45,45];; for n in [12..61] do a[n]:=a[n-1]+a[n-10]-a[n-11]; od; a; # G. C. Greubel, Aug 31 2019

I:=[0,1,3,6,10,15,21,28,36,45,45]; [n le 11 select I[n] else Self(n-1) + Self(n-10) - Self(n-11): n in [1..61]]; // G. C. Greubel, Aug 31 2019

seq(coeff(series(x*(1-10*x^9+9*x^10)/((1-x^10)*(1-x)^3), x, n+1), x, n), n = 0..60); # G. C. Greubel, Aug 31 2019

LinearRecurrence[{1,0,0,0,0,0,0,0,0,1,-1}, {0,1,3,6,10,15,21,28,36,45, 45}, 60] (* G. C. Greubel, Aug 31 2019 *)

a(n) = sum(k=0, n, k % 10); \\ Michel Marcus, Apr 28 2018

def A130488(n):
    a, b = divmod(n,10)
    return 45*a+(b*(b+1)>>1) # Chai Wah Wu, Jul 27 2022

def A130488_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P(x*(1-10*x^9+9*x^10)/((1-x^10)*(1-x)^3)).list()
A130488_list(60) # G. C. Greubel, Aug 31 2019

a(n) = 45*floor(n/10) + A010879(n)*(A010879(n) + 1)/2.
G.f.: (Sum_{k=1..9} k*x^k)/((1-x^10)*(1-x)).
G.f.: x*(1 - 10*x^9 + 9*x^10)/((1-x^10)*(1-x)^3).

A070365 a(n) = 5^n mod 7.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane, May 12 2002

From Klaus Brockhaus, May 23 2010: (Start)
Period 6: repeat [1, 5, 4, 6, 2, 3].
Continued fraction expansion of (221+11*sqrt(1086))/490.
Decimal expansion of 199/1287.
First bisection is A153727. (End)

G. C. Greubel, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,-1,1).

Cf. A178229 (decimal expansion of (221+11*sqrt(1086))/490), A178141 (repeat 4, -1, 2, -4, 1, -2), A117373 (repeat 1, -2, -3, -1, 2, 3), A153727 (trajectory of 3x+1 sequence starting at 1).

Cf. A000351, A010876.

[Modexp(5, n, 7): n in [0..100]]; // Vincenzo Librandi, Mar 24 2016 - after Bruno Berselli

A070365:=n->[1, 5, 4, 6, 2, 3][(n mod 6)+1]: seq(A070365(n), n=0..100); # Wesley Ivan Hurt, Jun 23 2016

PowerMod[5, Range[0, 110], 7] (* or *) LinearRecurrence[{1, 0, -1, 1}, {1, 5, 4, 6}, 110] (* Harvey P. Dale, Apr 26 2011 *)
Table[Mod[5^n, 7], {n, 0, 100}] (* G. C. Greubel, Mar 05 2016 *)
PadRight[{}, 100, {1, 5, 4, 6, 2, 3}] (* or *) CoefficientList[Series[(1 + 5 x + 4 x^2 + 6 x^3 + 2 x^4 + 3 x^5) / (1 - x^6), {x, 0, 100}], x] (* Vincenzo Librandi, Mar 24 2016 *)

a(n)=lift(Mod(5,7)^n) \\ Charles R Greathouse IV, Mar 22 2016

From R. J. Mathar, Apr 13 2010: (Start)
a(n) = a(n-1) - a(n-3) + a(n-4) for n>3.
G.f.: (1+4*x-x^2+3*x^3)/ ((1-x)*(1+x)*(x^2-x+1)). (End)
From Klaus Brockhaus, May 23 2010: (Start)
a(n+1)-a(n) = A178141(n).
a(n+2)-a(n) = A117373(n+5). (End)
From G. C. Greubel, Mar 05 2016: (Start)
a(n) = a(n-6) for n>5.
E.g.f.: (1/3)*(7*cosh(x) + 14*sinh(x) + 2*sqrt(3)*exp(x/2)*sin(sqrt(3)*x/2) - 4*exp(x/2)*cos(sqrt(3)*x/2)). (End)
a(n) = (21 - 7*cos(n*Pi) - 8*cos(n*Pi/3) + 4*sqrt(3)*sin(n*Pi/3))/6. - Wesley Ivan Hurt, Jun 23 2016
a(n) = A010876(A000351(n)). - Michel Marcus, Jun 27 2016

A010887 Simple periodic sequence: repeat 1,2,3,4,5,6,7,8.

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

Partial sums are given by A130486(n)+n+1. - Hieronymus Fischer, Jun 08 2007

1371742/11111111 = 0.123456781234567812345678... - Eric Desbiaux, Nov 03 2008

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,1).

Cf. A010872, A010873, A010874, A010875, A010876, A010878, A004526, A002264, A002265, A002266.

Cf. A177034 (decimal expansion of (9280+3*sqrt(13493990))/14165). - Klaus Brockhaus, May 01 2010

a010887 = (+ 1) . flip mod 8
a010887_list = cycle [1..8]
-- Reinhard Zumkeller, Nov 09 2014, Mar 04 2014

PadRight[{},90,Range[8]] (* Harvey P. Dale, May 10 2022 *)

def A010887(n): return 1 + (n & 7) # Chai Wah Wu, May 25 2022

a(n) = 1 + (n mod 8) - Paolo P. Lava, Nov 21 2006
From Hieronymus Fischer, Jun 08 2007: (Start)
a(n) = (1/2)*(9 - (-1)^n - 2*(-1)^(b/4) - 4*(-1)^((b - 2 + 2*(-1)^(b/4))/8)) where b = 2n - 1 + (-1)^n.
Also a(n) = A010877(n) + 1.
G.f.: g(x) = (1/(1-x^8))*Sum_{k=0..7} (k+1)*x^k.
Also: g(x) = (8x^9 - 9x^8 + 1)/((1-x^8)*(1-x)^2). (End)

A204453 Period length 14: [0, 1, 2, 3, 4, 5, 6, 0, 6, 5, 4, 3, 2, 1] repeated.

Original entry on oeis.org

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

Offset: 0

Wolfdieter Lang, Jan 17 2012

This sequence can be continued periodically for negative values of n, and then a(-n) = a(n).
This is the seventh sequence of a k-family of sequences P_k, k>=1, which starts with A000007(n+1), n>=0, (the 0-sequence), A000035, A193680, A193682, A203572, A for k=1..6, respectively.
See a comment on A203571 for the general case of the P_k sequences. For a(n)=P_7(n) the nonnegative members of the equivalence classes [0], [1],...,[6], defined by p==q iff P_7(p)=P_7(q), are found in the array A113807 if there the last class [7], starting with 7, is replaced by 0,7,14,..., to become the first class [0] (nonnegative part).

			a(16) = 16(mod 7) = 2 because 16\7 = floor(16/7)=2 is even; the sign is +1.
a(9) = (7-9)(mod 7) = 5 because 9\7 = floor(9/7)=1 is odd; the sign is -1.

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Cf. A203572 (k=6), A113807, A010876.

a(n) = n(mod 7) if (-1)^floor(n/7)=+1 else (7-n)(mod 7), n>=0. (-1)^floor(n/7) is the sign corresponding to the parity of the quotient floor(n/7). This quotient is sometimes denoted by n\7.
O.g.f.: x*(1+2*x+3*x^2+4*x^3+5*x^4+6*x^5+6*x^7+5*x^8+4*x^9+ 3*x^10+2*x^11+x^12)/(1-x^14).
a(n) = (7*m*(m^4-21*m^3+175*m^2-735*m+1624)*((-1)^floor(n/7)-1)-10908*(-1)^floor(n/7)+12348)*m/1440 where m = n-7*floor(n/7). - Luce ETIENNE, Oct 13 2017

A060154 Table T(n,k) by antidiagonals of n^k mod k [n,k >= 1].

Original entry on oeis.org

0, 1, 0, 1, 0, 0, 1, 2, 1, 0, 1, 0, 0, 0, 0, 1, 2, 1, 1, 1, 0, 1, 4, 3, 0, 2, 0, 0, 1, 2, 3, 4, 1, 0, 1, 0, 1, 0, 3, 4, 0, 0, 1, 0, 0, 1, 8, 1, 4, 1, 1, 1, 2, 1, 0, 1, 4, 0, 0, 5, 0, 2, 0, 0, 0, 0, 1, 2, 9, 1, 1, 6, 1, 3, 1, 1, 1, 0, 1, 4, 3, 6, 8, 0, 0, 4, 4, 0, 2, 0, 0, 1, 2, 9, 4, 5, 0, 1, 1, 3, 0, 1, 0, 1, 0

Offset: 1

Henry Bottomley, Mar 12 2001

			T(5,3) = 5^3 mod 3 = 125 mod 3 = 2.
Rows start:
  0, 1, 1, 1, 1, ...
  0, 0, 2, 0, 2, ...
  0, 1, 0, 1, 3, ...
  0, 0, 1, 0, 4, ...
  0, 1, 2, 1, 0, ...

Seiichi Manyama, Antidiagonals n = 1..140, flattened

Rows include A057427, A015910, A056969.
Columns include A000004, A000035 (several times), A010872, A010874, A010876, A021559 and other periodic sequences.
Diagonals include A000004 and A057427.
Cf. A114448.

T(n, k) = A051129(n, k)-n*A060155(n, k).

A130489 a(n) = Sum_{k=0..n} (k mod 11) (Partial sums of A010880).

Original entry on oeis.org

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 55, 56, 58, 61, 65, 70, 76, 83, 91, 100, 110, 110, 111, 113, 116, 120, 125, 131, 138, 146, 155, 165, 165, 166, 168, 171, 175, 180, 186, 193, 201, 210, 220, 220, 221, 223, 226, 230, 235, 241, 248, 256, 265, 275, 275, 276

Offset: 0

Hieronymus Fischer, May 31 2007

nonn

Let A be the Hessenberg n X n matrix defined by A[1,j] = j mod 11, A[i,i]:=1, A[i,i-1]=-1. Then, for n >= 1, a(n)=det(A). - Milan Janjic, Jan 24 2010

Shawn A. Broyles, Table of n, a(n) for n = 0..1000
Index entries for linear recurrences with constant coefficients, signature (1,0,0,0,0,0,0,0,0,0,1,-1).

Cf. A010872, A010873, A010874, A010875, A010876, A010877, A010878, A010879, A130481, A130482, A130483, A130484, A130485, A130486, A130487, A130488.

a:=[0,1,3,6,10,15,21,28,36,45, 55,55];; for n in [13..61] do a[n]:=a[n-1]+a[n-11]-a[n-12]; od; a; # G. C. Greubel, Aug 31 2019

I:=[0,1,3,6,10,15,21,28,36,45,55,55]; [n le 12 select I[n] else Self(n-1) + Self(n-11) - Self(n-12): n in [1..61]]; // G. C. Greubel, Aug 31 2019

seq(coeff(series(x*(1-11*x^10+10*x^11)/((1-x^11)*(1-x)^3), x, n+1), x, n), n = 0 .. 60); # G. C. Greubel, Aug 31 2019

LinearRecurrence[{1,0,0,0,0,0,0,0,0,0,1,-1}, {0,1,3,6,10,15,21,28,36,45, 55,55}, 60] (* G. C. Greubel, Aug 31 2019 *)
Accumulate[PadRight[{},80,Range[0,10]]] (* Harvey P. Dale, Jul 21 2021 *)

a(n) = sum(k=0, n, k % 11); \\ Michel Marcus, Apr 28 2018

def A130489_list(prec):
    P. = PowerSeriesRing(ZZ, prec)
    return P(x*(1-11*x^10+10*x^11)/((1-x^11)*(1-x)^3)).list()
A130489_list(60) # G. C. Greubel, Aug 31 2019

a(n) = 55*floor(n/11) + A010880(n)*(A010880(n) + 1)/2.
G.f.: (Sum_{k=1..10} k*x^k)/((1-x^11)*(1-x)).
G.f.: x*(1 - 11*x^10 + 10*x^11)/((1-x^11)*(1-x)^3).

A010885 Period 6: repeat [1, 2, 3, 4, 5, 6].

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

Partial sums are given by A130484(n)+n+1. - Hieronymus Fischer, Jun 08 2007

41152/333333 = 0.123456123456123456... [Eric Desbiaux, Nov 03 2008]

Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,1).

Cf. A010872, A010873, A010874, A010875, A010876, A004526, A002264, A002265, A002266.

Cf. A177158 (decimal expansion of (103+2*sqrt(4171))/162). [From Klaus Brockhaus, May 03 2010]

&cat[[1..6]: n in [0..20]]; // Wesley Ivan Hurt, Jun 17 2016

A010885:=n->(21-3*cos(n*Pi)-4*sqrt(3)*cos((1-4*n)*Pi/6)-12*sin((1+2*n)*Pi/6))/6: seq(A010885(n), n=0..100); # Wesley Ivan Hurt, Jun 17 2016

Flatten[Table[Range[6],{n,15}]] (* Harvey P. Dale, Aug 01 2011 *)
PadRight[{},90,Range[6]] (* Harvey P. Dale, Sep 23 2019 *)

a(n) = 1 + (n mod 6). - Paolo P. Lava, Nov 21 2006
a(n) = A010875(n)+1. G.f.: g(x)=(Sum_{0<=k<6} (k+1)*x^k)/(1-x^6). Also g(x)=(6*x^7-7*x^6+1)/((1-x^6)*(1-x)^2). - Hieronymus Fischer, Jun 08 2007
From Wesley Ivan Hurt, Jun 17 2016: (Start)
G.f.: (1+2*x+3*x^2+4*x^3+5*x^4+6*x^5)/(1-x^6).
a(n) = (21-3*cos(n*Pi)-4*sqrt(3)*cos((1-4*n)*Pi/6)-12*sin((1+2*n)*Pi/6))/6.
a(n) = a(n-6) for n>5. (End)

cp's OEIS Frontend

A130487 a(n) = Sum_{k=0..n} (k mod 9) (Partial sums of A010878).

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A010883 Simple periodic sequence: repeat 1,2,3,4.

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A099548 Odd part of n modulo 7.

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A130488 a(n) = Sum_{k=0..n} (k mod 10) (Partial sums of A010879).

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A070365 a(n) = 5^n mod 7.

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A010887 Simple periodic sequence: repeat 1,2,3,4,5,6,7,8.

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A204453 Period length 14: [0, 1, 2, 3, 4, 5, 6, 0, 6, 5, 4, 3, 2, 1] repeated.