A238186 - OEIS

%I #22 May 10 2021 09:57:28

%S 79,107,127,151,173,179,181,199,223,227,233,251,271,307,331,367,409,

%T 421,431,439,443,457,491,521,541,569,577,641,653,659,709,727,733,743,

%U 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

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

%C Subsequence of A091209 (see comments there).

%H Antti Karttunen, <a href="/A238186/b238186.txt">Table of n, a(n) for n = 1..33319; all terms up to binary length 20</a>

%H <a href="/index/Ge#GF2X">Index entries for sequences related to binary encoded polynomials over GF(2)</a>

%e 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

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

%Y Intersection of A000069 and A091209.

%Y Intersection of A027697 and A091242.

%Y Equals the set difference of A027697 and A091206.

%K nonn

%O 1,1

%A _Joerg Arndt_, Feb 19 2014