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

Author

Hieronymus Fischer, Sep 30 2007

Keywords

• nonn

Comments

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

Links

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

Crossrefs

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

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

Programs

Mathematica

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

PARI

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

PARI

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