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A238186
Primes with odd Hamming weight that as polynomials over GF(2) are reducible.
4
79, 107, 127, 151, 173, 179, 181, 199, 223, 227, 233, 251, 271, 307, 331, 367, 409, 421, 431, 439, 443, 457, 491, 521, 541, 569, 577, 641, 653, 659, 709, 727, 733, 743, 809, 823, 829, 919, 941, 947, 991, 997, 1009, 1021, 1087, 1109, 1129, 1171, 1187, 1201, 1213, 1231, 1249, 1259, 1301, 1321, 1327, 1361, 1373
OFFSET
1,1
COMMENTS
Subsequence of A091209 (see comments there).
EXAMPLE
79 is a term because 79 = 1001111_2 which corresponds to the polynomial x^6 + x^3 + x^2 + x + 1, but over GF(2) we have x^6 + x^3 + x^2 + x + 1 = (x^2 + x + 1)*(x^4 + x^3 + 1). - Jianing Song, May 10 2021
PROG
(PARI) forprime(p=2, 10^4, if( (hammingweight(p)%2==1) && ! polisirreducible( Mod(1, 2)*Pol(binary(p)) ), print1(p, ", ") ) );
CROSSREFS
Intersection of A000069 and A091209.
Intersection of A027697 and A091242.
Equals the set difference of A027697 and A091206.
Sequence in context: A139922 A112795 A107162 * A135143 A139503 A134240
KEYWORD
nonn
AUTHOR
Joerg Arndt, Feb 19 2014
STATUS
approved