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 A236861 Characteristic function of A236841 (A234741): a(n) = 1 if n is a result of downward remultiplication (N -> GF(2)[X]) of some number, 0 otherwise. 8
 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 1, 1, 1, 1, 1, 0, 1, 1, 1, 1, 0, 1, 0, 1, 1, 1 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0 LINKS Antti Karttunen, Table of n, a(n) for n = 0..8192 FORMULA a(0)=1, a(1)=1, a(p)=1 for primes p, and for composite n which are irreducible in GF(2)[X] (terms of A091214), a(n)=0, and for other composite n (terms of A091212), a(n) = 1 only if there exists at least one such pair of k, m < n that n = A048720(k,m) and a(k)*a(m) = 1, and 0 otherwise. (Please compare also to the formula for A236862). PROG (Scheme, two quite inefficient implementations, which require also definec and/or GF2Xdivide from a linked Scheme-source file) (definec (A236861 n) (if (zero? (A236833 n)) 0 1)) (definec (A236861 n) (cond ((< n 2) 1) ((prime? n) 1) ((= 1 (A091225 n)) 0) (else (let loop ((d 2)) (cond ((= d n) 0) ((and (= d (A091255bi n d)) (not (zero? (* (A236861 d) (A236861 (GF2Xdivide n d)))))) 1) (else (loop (+ d 1)))))))) CROSSREFS Positions of zeros occur in the same positions as in A236833; sequence A236834 gives these positions. Cf. A236841, A234741, A236862, A048720, A091225, A091255. Sequence in context: A296077 A322674 A256175 * A016300 A016126 A016068 Adjacent sequences:  A236858 A236859 A236860 * A236862 A236863 A236864 KEYWORD nonn AUTHOR Antti Karttunen, Apr 13 2014 STATUS approved

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Last modified August 22 07:17 EDT 2019. Contains 326172 sequences. (Running on oeis4.)