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

Author

T. D. Noe, Feb 26 2006

Keywords

• nonn

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).

Examples

			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.