A010876 -id:A010876 - cp's OEIS frontend

A010889 Simple periodic sequence: repeat 1,2,3,4,5,6,7,8,9,10.

1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 1

Offset: 0

N. J. A. Sloane

Partial sums are given by A130488(n)+n+1. - Hieronymus Fischer, Jun 08 2007

Continued fraction expansion of (232405+sqrt(71216963807))/348378. [From Klaus Brockhaus, May 15 2010]

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

Cf. A010872, A010873, A010874, A010875, A010876, A010877, A010878, A004526, A002264, A002265, A002266.

Cf. A177933 (decimal expansion of (232405+sqrt(71216963807))/348378). [From Klaus Brockhaus, May 15 2010]

PadRight[{},120,Range[10]] (* Harvey P. Dale, Feb 22 2015 *)

def a(n): return n % 10 + 1 # Paul Muljadi, Aug 06 2024

a(n) = 1 + (n mod 10) - Paolo P. Lava, Nov 21 2006
From Hieronymus Fischer, Jun 08 2007: (Start)
a(n) = A010879(n)+1.
G.f.: (Sum_{k=0..9} (k+1)*x^k)/(1-x^10).
G.f.: (10x^11-11x^10+1)/((1-x^10)(1-x)^2). (End)

More terms from Klaus Brockhaus, May 15 2010

A068909 Number of partitions of n modulo 7.

Original entry on oeis.org

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

Offset: 0

Henry Bottomley, Mar 05 2002

nonn

Of the partitions of numbers from 1 to 100000: 27193 are 0, 12078 are 1, 12203 are 2, 12260 are 3, 12231 are 4, 12003 are 5 and 12032 are 6 modulo 7, largely because the number of partitions of 7m+5 is always a multiple of 7.

Henry Bottomley, Partition calculators using java applets
Index entries for sequences related to partitions

Cf. A000041, A010876, A068906.

Cf. A040051, A068907, A068908, A020919.

Table[Mod[PartitionsP[n],7],{n,0,110}] (* Harvey P. Dale, Feb 17 2018 *)

a(n) = numbpart(n) % 7; \\ Michel Marcus, Jul 14 2022

a(n) = A010876(A000041(n)) = A068906(7, n).

a(n) = Pm(n,1) with Pm(n,k) = if kReinhard Zumkeller, Jun 09 2009]

A130490 a(n) = Sum_{k=0..n} (k mod 12) (Partial sums of A010881).

Original entry on oeis.org

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 66, 67, 69, 72, 76, 81, 87, 94, 102, 111, 121, 132, 132, 133, 135, 138, 142, 147, 153, 160, 168, 177, 187, 198, 198, 199, 201, 204, 208, 213, 219, 226, 234, 243, 253, 264, 264, 265, 267, 270, 274, 279, 285, 292, 300

Offset: 0

Hieronymus Fischer, May 31 2007

nonn

Let A be the Hessenberg n X n matrix defined by: A[1,j] = j mod 12, 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 (1,0,0,0,0,0,0,0,0,0,0,1,-1).

Cf. A010872, A010873, A010874, A010875, A010876, A010877, A010878, A010879, A010880, A130481, A130482, A130483, A130484, A130485, A130486, A130487, A130488, A130489.

List([0..60], n-> Sum([0..n], k-> k mod 12 )); # G. C. Greubel, Sep 01 2019

[&+[(k mod 12): k in [0..n]]: n in [0..60]]; // G. C. Greubel, Sep 01 2019

seq(coeff(series(x*(1-12*x^11+11*x^12)/((1-x^12)*(1-x)^3), x, n+1), x, n), n = 0..60); # G. C. Greubel, Sep 01 2019

Sum[Mod[k, 12], {k, 0, Range[0, 60]}] (* G. C. Greubel, Sep 01 2019 *)
LinearRecurrence[{1,0,0,0,0,0,0,0,0,0,0,1,-1},{0,1,3,6,10,15,21,28,36,45,55,66,66},60] (* Harvey P. Dale, Jan 16 2024 *)

a(n) = sum(k=0, n, k % 12); \\ Michel Marcus, Apr 29 2018

[sum(k%12 for k in (0..n)) for n in (0..60)] # G. C. Greubel, Sep 01 2019

a(n) = 66*floor(n/12) + A010881(n)*(A010881(n) + 1)/2.
G.f.: (Sum_{k=1..11} k*x^k)/((1-x^12)*(1-x)).
G.f.: x*(1 - 12*x^11 + 11*x^12)/((1-x^12)*(1-x)^3).

A010884 Period 5: repeat [1,2,3,4,5].

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

Partial sums are given by A130483(n)+n+1. - Hieronymus Fischer, Jun 08 2007

4115/33333 = 0.12345123451234512345... - Eric Desbiaux, Nov 03 2008

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

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

Cf. A177038 (decimal expansion of (195+sqrt(65029))/314).

PadRight[{},120,Range[5]] (* Harvey P. Dale, Dec 08 2018 *)

a(n)=n%5+1 \\ Charles R Greathouse IV, Jul 13 2016

a(n) = 1 + (n mod 5). - Paolo P. Lava, Nov 21 2006
From Hieronymus Fischer, Jun 08 2007: (Start)
G.f.: (5*x^4+4*x^3+3*x^2+2*x+1)/(1-x^5) = (5*x^6-6*x^5+1)/((1-x^5)*(1-x)^2).
a(n) = A010874(n)+1. (End)
a(n) = a(n-5). - Wesley Ivan Hurt, Jan 15 2022

A053842 (Sum of digits of n written in base 7) modulo 7.

Original entry on oeis.org

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

Offset: 0

Henry Bottomley, Mar 28 2000

a(n) is the sixth row of the array in A141803. - Andrey Zabolotskiy, May 18 2016

G. C. Greubel, Table of n, a(n) for n = 0..5000
Robert Walker, Self Similar Sloth Canon Number Sequences

Cf. A010876, A053828, A141803.

Cf. A010060, A053837-A053844.

Table[Mod[Plus @@ IntegerDigits[n, 7], 7], {n, 0, 50}] (* G. C. Greubel, Nov 02 2017 *)

a(n) = vecsum(digits(n, 7)) % 7; \\ Michel Marcus, May 18 2016

a(n) = A010876(A053828(n)). - Andrey Zabolotskiy, May 18 2016

A130910 Sum {0<=k<=n, k mod 16} (Partial sums of A130909).

Original entry on oeis.org

0, 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, 66, 78, 91, 105, 120, 120, 121, 123, 126, 130, 135, 141, 148, 156, 165, 175, 186, 198, 211, 225, 240, 240, 241, 243, 246, 250, 255, 261, 268, 276, 285, 295, 306, 318, 331, 345, 360, 360, 361, 363, 366, 370, 375, 381, 388

Offset: 0

Hieronymus Fischer, Jun 11 2007

nonn

Harvey P. Dale, Table of n, a(n) for n = 0..1000

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

Accumulate[Mod[Range[0,60],16]] (* Harvey P. Dale, May 30 2020 *)

a(n)=120*floor(n/16)+A130909(n)*(A130909(n)+1)/2. - G.f.: g(x)=(sum{1<=k<16, k*x^k})/((1-x^16)(1-x)). Also: g(x)=x(15x^16-16x^15+1)/((1-x^16)(1-x)^3).

a(n) = +a(n-1) +a(n-16) -a(n-17). G.f. ( x*(1 +2*x +3*x^2 +4*x^3 +5*x^4 +6*x^5 +7*x^6 +8*x^7 +9*x^8 +10*x^9 +11*x^10 +12*x^11 +13*x^12 +14*x^13 +15*x^14) ) / ( (1+x) *(1+x^2) *(1+x^4) *(1+x^8) *(x-1)^2 ). - R. J. Mathar, Nov 05 2011

A272647 a(n) = A001517(n) mod 7.

Original entry on oeis.org

1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1, 1, 3, 5, 4, 5, 3, 1

Offset: 0

N. J. A. Sloane, May 09 2016

Periodic with period length 7.

Colin Barker, Table of n, a(n) for n = 0..1000
D. H. Lehmer, Arithmetical periodicities of Bessel functions, Annals of Mathematics, 33 (1932): 143-150. The sequence is on page 149.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,1).

Cf. A001517, A002119, A272648.

Cf. A010876.

f:=proc(n) option remember; if n = 0 then 1 elif n=1 then 3 else f(n-2)+(4*n-2)*f(n-1); fi; end;
[seq(f(n) mod 7, n=0..120)];

PadRight[{},120,{1,3,5,4,5,3,1}] (* Harvey P. Dale, Jul 17 2020 *)

Vec((1+3*x+5*x^2+4*x^3+5*x^4+3*x^5+x^6)/((1-x)*(1+x+x^2+x^3+x^4+x^5+x^6)) + O(x^50)) \\ Colin Barker, May 10 2016

G.f.: (1 + 3*x + 5*x^2 + 4*x^3 + 5*x^4 + 3*x^5 + x^6) / ((1 - x)*(1 + x + x^2 + x^3 + x^4 + x^5 + x^6)). - Colin Barker, May 10 2016

a(n) = (3*m^6 - 54*m^5 + 365*m^4 - 1140*m^3 + 1582*m^2 - 636*m + 60)/60, where m = n mod 7. - Luce ETIENNE, Oct 18 2018

A272648 a(n) = A002119(n) mod 7.

Original entry on oeis.org

1, 1, 0, 1, 0, 1, 1, 6, 6, 0, 6, 0, 6, 6, 1, 1, 0, 1, 0, 1, 1, 6, 6, 0, 6, 0, 6, 6, 1, 1, 0, 1, 0, 1, 1, 6, 6, 0, 6, 0, 6, 6, 1, 1, 0, 1, 0, 1, 1, 6, 6, 0, 6, 0, 6, 6, 1, 1, 0, 1, 0, 1, 1, 6, 6, 0, 6, 0, 6, 6, 1, 1, 0, 1, 0, 1, 1, 6, 6, 0, 6

Offset: 0

N. J. A. Sloane, May 09 2016

Periodic with period 14.

Colin Barker, Table of n, a(n) for n = 0..1000
D. H. Lehmer, Arithmetical periodicities of Bessel functions, Annals of Mathematics, 33 (1932): 143-150. The sequence is on page 149.
Index entries for linear recurrences with constant coefficients, signature (0,0,0,0,0,0,0,0,0,0,0,0,0,1).

Cf. A001517, A002119, A272647.

Cf. A010876.

b:=[1,-1];; for n in [3..95] do b[n]:=-2*(2*n-3)*b[n-1]+b[n-2]; od; a:=List(b,AbsInt) mod 7; # Muniru A Asiru, Sep 20 2018

f:=proc(n) option remember; if n = 0 then 1 elif n=1 then 1 else f(n-2)+(4*n-2)*f(n-1); fi; end;
[seq(f(n) mod 7, n=0..120)];

PadRight[{},120,{1,1,0,1,0,1,1,6,6,0,6,0,6,6}] (* Harvey P. Dale, Jun 07 2016 *)

Vec((1+x+x^3+x^5+x^6)*(1+6*x^7)/((1-x)*(1+x)*(1-x+x^2-x^3+x^4-x^5+x^6)*(1+x+x^2+x^3+x^4+x^5+x^6)) + O(x^50)) \\ Colin Barker, May 10 2016

G.f.: (1+x+x^3+x^5+x^6)*(1+6*x^7) / ((1-x)*(1+x)*(1-x+x^2-x^3+x^4-x^5+x^6)*(1+x+x^2+x^3+x^4+x^5+x^6)). - Colin Barker, May 10 2016

a(n) = (-m^6+18*m^5-122*m^4+384*m^3-549*m^2+270*m+24)*(7-5*(-1)^floor(n/7))/48, where m = (n mod 7). - Luce ETIENNE, Sep 21 2018

A279316 Period 7: repeat [0, 1, 2, 3, 3, 2, 1].

Original entry on oeis.org

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

Offset: 0

Wesley Ivan Hurt, Dec 09 2016

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

Cf. A279313.

Cf. A010876.

&cat[[0, 1, 2, 3, 3, 2, 1]: n in [0..10]];

a:=n->[0, 1, 2, 3, 3, 2, 1][(n mod 7)+1]: seq(a(n), n=0..300);

CoefficientList[Series[x*(1 + 2*x + 3*x^2 + 3*x^3 + 2*x^4 + x^5)/(1 - x^7), {x, 0, 100}], x]
PadRight[{}, 120, {0, 1, 2, 3, 3, 2, 1}] (* Vincenzo Librandi, Dec 10 2016 *)

G.f.: x*(1 + 2*x + 3*x^2 + 3*x^3 + 2*x^4 + x^5)/(1 - x^7).
a(n) = (1/2) * Sum_{i=1..2n} (-1)^floor((i-1)/7).
a(n) = a(n-7) for n > 6.
a(n) = A279313(2n)/2.
a(n) = -m*(m^5 - 21*m^4 + 160*m^3 - 525*m^2 + 739*m - 714)/360 where m = n mod 7. - Luce ETIENNE, Nov 18 2018

A010886 Period 7: repeat [1, 2, 3, 4, 5, 6, 7].

Original entry on oeis.org

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

Offset: 0

N. J. A. Sloane

Partial sums are given by A130485(n)+n+1. - Hieronymus Fischer, Jun 08 2007

Decimal expansion of 1234567/9999999 = 0.123456712345671234567... - Eric Desbiaux, Nov 03 2008

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

Cf. A002264, A002265, A002266, A004526, A010872, A010873, A010874, A010875, A010876, A010877, A130485.

Cf. A177160 (decimal expansion of (4502+sqrt(29964677))/6961).

&cat [[1, 2, 3, 4, 5, 6, 7]^^20]; // Wesley Ivan Hurt, Jul 18 2016

seq(op([1, 2, 3, 4, 5, 6, 7]), n=0..20); # Wesley Ivan Hurt, Jul 18 2016

PadRight[{}, 100, {1, 2, 3, 4, 5, 6, 7}] (* Wesley Ivan Hurt, Jul 18 2016 *)

a(n)=n%7+1 \\ Charles R Greathouse IV, Jul 13 2016

a(n) = 1 + (n mod 7). - Paolo P. Lava, Nov 21 2006
a(n) = A010876(n) + 1. G.f.: (Sum_{k=0..6} (k+1)*x^k)/(1-x^7). Also (7*x^8-8*x^7+1)/((1-x^7)*(1-x)^2). - Hieronymus Fischer, Jun 08 2007
From Wesley Ivan Hurt, Jul 18 2016: (Start)
a(n) = a(n-7) for n>6.
a(n) = 1 - 6*floor(n/7) + Sum_{k=1..6} floor((n + k)/7). (End)

cp's OEIS Frontend

A010889 Simple periodic sequence: repeat 1,2,3,4,5,6,7,8,9,10.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

Python

Formula

Extensions

A068909 Number of partitions of n modulo 7.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A130490 a(n) = Sum_{k=0..n} (k mod 12) (Partial sums of A010881).

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

GAP

Magma

Maple

Mathematica

PARI

Sage

Formula

A010884 Period 5: repeat [1,2,3,4,5].

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A053842 (Sum of digits of n written in base 7) modulo 7.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Mathematica

PARI

Formula

A130910 Sum {0<=k<=n, k mod 16} (Partial sums of A130909).

Views

Author

Keywords

Links

Crossrefs

Programs

Mathematica

Formula

A272647 a(n) = A001517(n) mod 7.

Views

Author

Keywords

Comments

Links

Crossrefs

Programs

Maple

Mathematica