A304108 Numbers n such that the (0,1)-polynomial encoded in binary expansion of n has at least one duplicated irreducible divisor when the factorization is done in polynomial ring GF(2)[X].

4, 5, 8, 10, 12, 15, 16, 17, 20, 21, 24, 27, 28, 30, 32, 34, 36, 39, 40, 42, 44, 45, 48, 51, 52, 54, 56, 57, 60, 63, 64, 65, 68, 69, 72, 75, 76, 78, 80, 81, 84, 85, 88, 90, 92, 95, 96, 99, 100, 102, 104, 105, 107, 108, 112, 114, 116, 119, 120, 124, 125, 126, 128, 130, 132, 135, 136, 138, 140, 141, 144, 147, 148, 150, 151, 152, 153, 156, 160, 162

Offset: 1

Author

Antti Karttunen, May 13 2018

Keywords

• nonn

Comments

Positions of zeros in A091219 and A304109. Numbers n such that A091221(n) < A091222(n).

Examples

			4 is present as 4 = A048720(2,2) = A048720(A014580(1), A014580(1)).
5 is present as 5 = A048720(3,3) = A048720(A014580(2), A014580(2)).
10 is present as 10 = A048720(2,A048720(3,3)).
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..32768
• Index entries for sequences related to polynomials in ring GF(2)[X]

Crossrefs

Cf. A304107 (complement).

Cf. A014580, A048720, A091219, A091221, A091222, A304109.

Cf. also A013929.

Programs

PARI

isA304108(n) = { my(fm=factor(Pol(binary(n))*Mod(1, 2))); for(k=1, #fm~, if(fm[k, 2] > 1, return(1))); (0); };
k=0; n=0; while(k<100, n++; if(isA304108(n), k++; print1(n,", ")));