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 A236851 Remultiply n first "upward", from GF(2)[X] to N, and then remultiply that result back "downward", from N to GF(2)[X]: a(n) = A234741(A234742(n)). 6
 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 17, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 51, 44, 45, 46, 47, 48, 49, 34, 51, 52, 53, 54, 39, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Antti Karttunen, Table of n, a(n) for n = 0..8192 FORMULA a(n) = A234741(A234742(n)). To compute a(n): factor n as a polynomial over GF(2) (where n is mapped to such polynomials via the binary representation of n), that is, find first a unique multiset of terms i, j, ..., k from A014580 for which i x j x ... x k = n, where x stands for the carryless multiplication (A048720). Then divide from those i, j, ..., k the ones that are in A091214 (composite integers in N) to their constituent prime factors (in N), and multiply all back together (including the factors that are in A091206 and thus not changed) with the carryless multiplication (A048720). Compare this to how primes are "broken" in a similar way in A235027 (cf. also A235145). EXAMPLE 5 ('101' in binary) = 3 x 3 (3 = '11' in binary). 3 is in A091206, so it stays intact, and 3 x 3 = 5, thus a(5)=5. 25 ('11001' in binary) = 25 (25 is irreducible in GF(2)[X]). However, it divides as 5*5 in Z, so the result is 5 x 5 = 17, thus a(25)=17, 25 being the least n which is not fixed by this function. 43 ('101011' in binary) = 3 x 25, of which the latter factor divides to 5*5, thus the result is 3 x 5 x 5 = 3 x 17 = 15 x 5 = 51. PROG (Scheme) (define (A236851 n) (A234741 (A234742 n))) CROSSREFS A236850 gives the fixed points. Cf. A234741, A234742, A236380, A236852, A236836-A236837, A236846-A236847. Sequence in context: A172275 A025484 A325383 * A030545 A295886 A318893 Adjacent sequences:  A236848 A236849 A236850 * A236852 A236853 A236854 KEYWORD nonn AUTHOR Antti Karttunen, Feb 02 2014 STATUS approved

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Last modified February 29 05:25 EST 2020. Contains 332353 sequences. (Running on oeis4.)