A238186 Primes with odd Hamming weight that as polynomials over GF(2) are reducible.

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

Author

Joerg Arndt, Feb 19 2014

Keywords

• nonn

Comments

Subsequence of A091209 (see comments there).

Examples

			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
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..33319; all terms up to binary length 20
• Index entries for sequences related to binary encoded polynomials over GF(2)

Crossrefs

Intersection of A000069 and A091209.

Intersection of A027697 and A091242.

Equals the set difference of A027697 and A091206.

Programs

PARI

forprime(p=2, 10^4, if( (hammingweight(p)%2==1) && ! polisirreducible( Mod(1,2)*Pol(binary(p)) ), print1(p,", ") ) );