This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A091209 #38 Feb 28 2016 14:05:22
%S A091209 5,17,23,29,43,53,71,79,83,89,101,107,113,127,139,149,151,163,173,179,
%T A091209 181,197,199,223,227,233,251,257,263,269,271,277,281,293,307,311,317,
%U A091209 331,337,347,349,353,359,367,373,383,389,401,409,421,431,439,443,449,457,461,467,479,491,503,509,521,523
%N A091209 Primes whose binary representation encodes a polynomial reducible over GF(2).
%C A091209 "Encoded in binary representation" means that a polynomial a(n)*X^n+...+a(0)*X^0 over GF(2) is represented by the binary number a(n)*2^n+...+a(0)*2^0 in Z (where each coefficient a(k) = 0 or 1).
%C A091209 Except for 3, all primes with even Hamming weight (A027699) are terms, see A238186 for the subsequence of primes with odd Hamming weight. [_Joerg Arndt_ and _Antti Karttunen_, Feb 19 2014]
%H A091209 Antti Karttunen, <a href="/A091209/b091209.txt">Table of n, a(n) for n = 1..71800</a>
%H A091209 A. Karttunen, <a href="/A091247/a091247.scm.txt">Scheme-program for computing this sequence.</a>
%H A091209 <a href="/index/Ge#GF2X">Index entries for sequences related to binary encoded polynomials over GF(2)</a>
%F A091209 a(n) = A000040(A091210(n)) = A091242(A091211(n)).
%F A091209 Other identities. For all n >= 1:
%F A091209 A235043(a(n)) = n. [A235043 works as a left inverse of this sequence.]
%p A091209 Primes:= select(isprime,[2,seq(2*i+1,i=1..1000)]):
%p A091209 filter:= proc(n) local L,x;
%p A091209 L:= convert(n,base,2);
%p A091209 Irreduc(add(L[i]*x^(i-1),i=1..nops(L))) mod 2;
%p A091209 end proc:
%p A091209 remove(filter,Primes); # _Robert Israel_, May 17 2015
%t A091209 Select[Prime[Range[2, 100]], !IrreduciblePolynomialQ[bb = IntegerDigits[#, 2]; Sum[bb[[k]] x^(k-1), {k, 1, Length[bb]}], Modulus -> 2]&] (* _Jean-François Alcover_, Feb 28 2016 *)
%o A091209 (PARI) forprime(p=2, 10^3, if( ! polisirreducible( Mod(1,2)*Pol(binary(p)) ), print1(p,", ") ) ); \\ _Joerg Arndt_, Feb 19 2014
%Y A091209 Intersection of A000040 and A091242.
%Y A091209 Disjoint union of A238186 and (A027699 \ {3}).
%Y A091209 Left inverse: A235043.
%Y A091209 Cf. A091206 (Primes whose binary expansion encodes a polynomial irreducible over GF(2)), A091212 (Composite, and reducible over GF(2)), A091214 (Composite, but irreducible over GF(2)).
%Y A091209 Cf. also A235041-A235042, A234742.
%K A091209 nonn
%O A091209 1,1
%A A091209 _Antti Karttunen_, Jan 03 2004