A238186 - OEIS

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

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OFFSET

1,1

COMMENTS

Subsequence of A091209 (see comments there).

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)

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

Adjacent sequences: A238183 A238184 A238185 * A238187 A238188 A238189

KEYWORD

nonn

AUTHOR

Joerg Arndt, Feb 19 2014

STATUS

approved