A133876 -id:A133876 - cp's OEIS frontend

A133636 Nonprime numbers k such that binomial(k+p,k) mod k = 1, where p=6.

9, 27, 49, 63, 77, 81, 91, 99, 117, 119, 121, 133, 143, 153, 161, 169, 171, 187, 189, 203, 207, 209, 217, 221, 243, 247, 253, 259, 261, 279, 287, 289, 297, 299, 301, 319, 323, 329, 333, 341, 343, 351, 361, 369, 371, 377, 387, 391, 403, 407, 413, 423, 427, 437

Offset: 1

Hieronymus Fischer, Sep 30 2007

nonn

Also composite n such that binomial(7*n,7)== n (mod n^2). - Gary Detlefs, Sep 24 2013

Harvey P. Dale, Table of n, a(n) for n = 1..1000

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

Cf. A133876, A133886, A133880, A133890, A133900, A133910.

Select[Range[500],CompositeQ[#]&&Mod[Binomial[#+6,#],#]==1&] (* Harvey P. Dale, Jan 30 2025 *)

isok(n) = ! isprime(n) && ((binomial(n+6, n) % n) == 1); \\ Michel Marcus, Sep 25 2013

isok(n) = ! isprime(n) && ((binomial(7*n, 7) % n^2) == n); \\ Michel Marcus, Sep 25 2013

A133886 a(n) = binomial(n+6,n) mod 6.

Original entry on oeis.org

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

Offset: 0

Hieronymus Fischer, Oct 10 2007

Periodic with length 2*6^2 = 72.

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

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

Cf. A133876, A133880, A133890, A133900, A133910.

A133886:=n->binomial(n+6,6) mod 6; seq(A133886(n), n=0..100); # Wesley Ivan Hurt, Apr 30 2014

Table[Mod[Binomial[n+6,n],6],{n,0,110}] (* Harvey P. Dale, May 04 2013 *)

a(n) = binomial(n+6,6) mod 6.
G.f.: g(x) = (1+x+4*x^2-6*x^9-6*x^56+4*x^63+x^64+x^65+3*x^8*(1+x)(1-x^56)/(1-x^8)+4*x^9(1+x+x^2)(1-x^54)/(1-x^9))/(1-x^72).
a(n) = a(n-1)-a(n-2)+a(n-8)+a(n-11)-a(n-17)-a(n-20)-a(n-24)+a(n-25)+a(n-29)+ a(n-32)- a(n-38)-a(n-41)+a(n-47)-a(n-48)+a(n-49). - Harvey P. Dale, May 04 2013

A133896 Numbers m such that binomial(m+6,m) mod 6 = 0.

Original entry on oeis.org

3, 4, 5, 6, 7, 12, 13, 14, 15, 21, 22, 23, 26, 30, 31, 34, 35, 39, 42, 43, 44, 50, 51, 52, 53, 58, 59, 60, 61, 62, 66, 67, 68, 69, 70, 71, 75, 76, 77, 78, 79, 84, 85, 86, 87, 93, 94, 95, 98, 102, 103, 106, 107, 111, 114, 115, 116, 122, 123, 124, 125, 130, 131, 132, 133, 134

Offset: 0

Hieronymus Fischer, Oct 20 2007

nonn

Partial sums of the sequence 3,1,1,1,1,5,1,1,1,6,1,1,3,4,1,3,1,4,3,1,1,6,1,1,1,5,1,1,1,1,4,1,1,1,1,1,4, ... which has period 36.

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

Cf. A133876, A133886, A133890, A133900, A133910.

Select[Range[140], Mod[Binomial[# + 6, #], 6] == 0&] (* Jean-François Alcover, Nov 12 2017 *)

isok(n) = !(binomial(n+6, n) % 6); \\ Michel Marcus, Nov 12 2017

G.f.: g(x)=3/(1-x)+ x/(1-x)^2+(4x^5+5x^9+2x^12+3x^13+2x^15+3x^17+2x^18+5x^21+3x^26+3x^32) /((1-x^36)(1-x)).

G.f.: g(x)=(3-2x+4x^5+5x^9+2x^12+3x^13+2x^15+3x^17+2x^18+5x^21+3x^26+3x^32-x^37) /((1-x^36)(1-x)^2).

cp's OEIS Frontend

A133636 Nonprime numbers k such that binomial(k+p,k) mod k = 1, where p=6.

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A133886 a(n) = binomial(n+6,n) mod 6.

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A133896 Numbers m such that binomial(m+6,m) mod 6 = 0.

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