A116926 Semiprimes k=p*q such that the polynomial (1+x)^k (mod k) has p+q nonzero terms.

6, 14, 15, 51, 62, 91, 95, 159, 254, 287, 473, 679, 703, 1139, 1199, 1339, 1717, 1891, 2051, 2147, 2495, 2651, 2701, 2869, 3151, 4313, 4381, 4607, 5017, 5267, 6245, 6683, 8441, 9809, 10063, 10637, 11051, 11183, 12403, 13119, 13169, 13207, 13423, 13427

Offset

1,1

Comments

The maximum number of nonzero terms is p+q; all powers of x of the form k*p and l*q for k=0..q-1 and l=1..p. The even terms of this sequence are twice the Mersenne primes: 2*3, 2*7, 2*31, 2*127, 2*8191,... Similarly, for terms divisible by 3, the other prime factor has the form 2*3^k-1. Note that A007012 gives the number of nonzero terms in the polynomial (1+x)^n (mod n).

Links

Table of n, a(n) for n=1..44.

Example

15 is here because (1+x)^15 (mod 15) = 1+5x^3+3x^5+10x^6+10x^9+3x^10+5x^12+x^15 has 3+5 nonzero terms.

Crossrefs

Cf. A007012.

Sequence in context: A218005 A337384 A063600 * A140330 A242832 A114634

Adjacent sequences: A116923 A116924 A116925 * A116927 A116928 A116929

Keyword

nonn

Author

T. D. Noe, Feb 26 2006

Status

approved