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 A091214 Composite numbers whose binary representation encodes a polynomial irreducible over GF(2). 21
 25, 55, 87, 91, 115, 117, 143, 145, 171, 185, 203, 213, 247, 253, 285, 299, 301, 319, 333, 351, 355, 357, 361, 369, 375, 391, 395, 415, 425, 445, 451, 471, 477, 501, 505, 515, 529, 535, 539, 545, 623, 637, 665, 675, 687, 695, 721, 731, 789, 799, 803, 817 (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). LINKS Antti Karttunen, Table of n, a(n) for n = 1..48410; all terms up to binary length 20 A. Karttunen, Scheme-program for computing beginning of this sequence. FORMULA Other identities. For all n >= 1: A235044(a(n)) = n. [A235044 works as a left inverse of this sequence.] a(n) = A014580(A091215(n)). - Antti Karttunen, May 17 2015 MATHEMATICA fQ[n_] := Block[{ply = Plus @@ (Reverse@ IntegerDigits[n, 2] x^Range[0, Floor@ Log2@ n])}, ply == Factor[ply, Modulus -> 2] && n != 2^Floor@ Log2@ n && ! PrimeQ@ n]; Select[ Range@ 840, fQ] (* Robert G. Wilson v, Aug 12 2011 *) PROG (PARI) isA014580(n)=polisirreducible(Pol(binary(n))*Mod(1, 2)); \\ This function from Charles R Greathouse IV isA091214(n) = (!isprime(n) && isA014580(n)); n = 0; i = 0; while(n < 2^20, n++; if(isA091214(n), i++; write("b091214.txt", i, " ", n))); \\ The b-file was computed with this program. Antti Karttunen, May 17 2015 CROSSREFS Intersection of A002808 and A014580. Subsequence of A235033, A236834 and A236838. Left inverse: A235044. Cf. A091206 (Primes whose binary expansion encodes a polynomial irreducible over GF(2)), A091209 (Primes that encode a polynomial reducible over GF(2)), A091212 (Composite, and reducible over GF(2)). Cf. A091215, A235027, A235046, A236841, A236845, A236850, A236851, A236861. Cf. also A235041-A235042. Sequence in context: A176275 A108166 A080863 * A036305 A257708 A266817 Adjacent sequences:  A091211 A091212 A091213 * A091215 A091216 A091217 KEYWORD nonn AUTHOR Antti Karttunen, Jan 03 2004 EXTENSIONS Entry revised and name corrected by Antti Karttunen, May 17 2015 STATUS approved

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Last modified October 20 05:31 EDT 2018. Contains 316378 sequences. (Running on oeis4.)