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Polynomials over GF(2) that are divisible by (x+1)^2 = x^2+1, encoded as binary numbers.
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%I #25 Jul 23 2022 19:27:56

%S 0,5,10,15,17,20,27,30,34,39,40,45,51,54,57,60,65,68,75,78,80,85,90,

%T 95,99,102,105,108,114,119,120,125,130,135,136,141,147,150,153,156,

%U 160,165,170,175,177,180,187,190,195,198,201,204,210,215,216,221,225,228,235

%N Polynomials over GF(2) that are divisible by (x+1)^2 = x^2+1, encoded as binary numbers.

%C Terms of A048725, sorted.

%C See also A001969 for those divisible by x+1 (and obviously the present sequence is a subsequence of that one).

%C From _Kevin Ryde_, Jul 22 2022: (Start)

%C Integers with an even number of 1-bits at even positions, and an even number of 1-bits at odd positions, and so all k with A355487(k) = 0.

%C Among four integers 4*i ..4*i+3, exactly one is a term here so that a(n) can be calculated by appending two bits to n-1 to ensure the two 1-bit counts are even, so a(n) = 4*(n-1) + A355487(n-1).

%C (End)

%o (PARI) a(n) = n--; n<<2 + if(n,fold(bitxor,digits(n,4))); \\ _Kevin Ryde_, Jul 01 2022

%Y Cf. A001969, A048725.

%Y Cf. A355487 (mod 4), A341389 (mod 2).

%K nonn,easy

%O 1,2

%A _Jack Zhang_, Apr 28 2022

%E More terms from _David A. Corneth_, Apr 28 2022