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A091212 Composite numbers whose binary representation encodes a polynomial reducible over GF(2). 13
4, 6, 8, 9, 10, 12, 14, 15, 16, 18, 20, 21, 22, 24, 26, 27, 28, 30, 32, 33, 34, 35, 36, 38, 39, 40, 42, 44, 45, 46, 48, 49, 50, 51, 52, 54, 56, 57, 58, 60, 62, 63, 64, 65, 66, 68, 69, 70, 72, 74, 75, 76, 77, 78, 80, 81, 82, 84, 85, 86, 88, 90, 92, 93, 94, 95, 96, 98, 99 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
"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).
From Reinhard Zumkeller, Jul 05-12 2011, values for maximum n corrected by Antti Karttunen, May 18 2015: (Start)
a(n) = A192506(n) for n <= 36.
a(n) = A175526(n) for n <= 36.
(End)
LINKS
FORMULA
a(n) = A091242(A091213(n)).
PROG
(PARI)
isA014580(n)=polisirreducible(Pol(binary(n))*Mod(1, 2)); \\ This function from Charles R Greathouse IV
isA091212(n) = ((n > 1) && !isprime(n) && !isA014580(n));
n = 0; i = 0; while(n < 2^16, n++; if(isA091212(n), i++; write("b091212.txt", i, " ", n)));
CROSSREFS
Intersection of A002808 and A091242.
Cf. A257688 (complement, either 1, irreducible in GF(2)[X] or prime), A091206 (prime and irreducible), A091209 (prime and reducible), A091214 (nonprime and irreducible).
Cf. A091213, A236861, A235036 (a subsequence, apart from 1).
Differs from both A175526 and A192506 for the first time at n=37, where a(37) = 56, while A175526(37) = A192506(37) = 55, a term missing from here (as 55 encodes a polynomial which is irreducible in GF(2)[X]).
Differs from its subsequence A205783(n+1) for the first time at n=47, where a(47) = 69, while 69 is missing from A205783.
Sequence in context: A115683 A175526 A192506 * A205783 A077094 A210441
KEYWORD
nonn
AUTHOR
Antti Karttunen, Jan 03 2004
STATUS
approved

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Last modified June 13 22:21 EDT 2024. Contains 373391 sequences. (Running on oeis4.)