A133887 -id:A133887 - cp's OEIS frontend

A133877 n modulo 7 repeated 7 times.

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

Offset: 0

Hieronymus Fischer, Oct 10 2007

nonn

Periodic with length 7^2=49.

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

Cf. A000040, A133620-A133625, A133630, A038509, A133634-A133636.

Cf. A133887, A133880, A133890, A133900, A133910.

a(n)=(1+floor(n/7)) mod 7.
a(n)=1+floor(n/7)-7*floor((n+7)/49).
a(n)=(((n+7) mod 49)-(n mod 7))/7.
a(n)=((n+7-(n mod 7))/7) mod 7.
a(n)=binomial(n+7,n) mod 7 =binomial(n+7,7) mod 7.
G.f. g(x)=(1-x^7)(1+2x^7+3x^14+4x^21+5x^28+6x^35)/((1-x)(1-x^49)).
G.f. g(x)=(6x^49-7x^42+1)/((1-x)(1-x^7)(1-x^49)).

A133897 Numbers m such that binomial(m+7,m) mod 7 = 0.

Original entry on oeis.org

42, 43, 44, 45, 46, 47, 48, 91, 92, 93, 94, 95, 96, 97, 140, 141, 142, 143, 144, 145, 146, 189, 190, 191, 192, 193, 194, 195, 238, 239, 240, 241, 242, 243, 244, 287, 288, 289, 290, 291, 292, 293, 336, 337, 338, 339, 340, 341, 342, 385, 386, 387, 388, 389, 390

Offset: 0

Hieronymus Fischer, Oct 20 2007

Also numbers m such that floor(1+(m/7)) mod 7 = 0.

Partial sums of the sequence 42,1,1,1,1,1,1,43,1,1,1,1,1,1,43,... which has period 7.

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

Cf. A000040, A133620, A133621, A133623, A133630, A133635.

Cf. A133877, A133887, A133890, A133900, A133910.

Select[Range[390],Mod[Binomial[#+7,#],7]==0&] (* or *) LinearRecurrence[{1,0,0,0,0,0,1,-1},{42, 43, 44, 45, 46, 47, 48, 91},55] (* James C. McMahon, Mar 30 2025 *)

a(n) = 7*n + 42 - 6*(n mod 7).
G.f.: (42+x+x^2+x^3+x^4+x^5+x^6+x^7)/((1-x^7)(1-x)).
G.f.: (42-41x-x^8) /((1-x^7)(1-x)^2).

cp's OEIS Frontend

A133877 n modulo 7 repeated 7 times.

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