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A116926
Semiprimes k=p*q such that the polynomial (1+x)^k (mod k) has p+q nonzero terms.
0
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).
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
KEYWORD
nonn
AUTHOR
T. D. Noe, Feb 26 2006
STATUS
approved