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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.
(history; published version)

#12 by N. J. A. Sloane at Thu May 15 10:19:05 EDT 2014

STATUS

editing

approved

#11 by N. J. A. Sloane at Thu May 15 10:19:02 EDT 2014

NAME

Characteristic function for of A236841 (A234741): a(n) = 1, if n is a result of downward remultiplication (N -> GF(2)[X]) of some number, 0 otherwise.

STATUS

proposed

editing

#10 by Antti Karttunen at Sat Apr 26 14:52:16 EDT 2014

STATUS

editing

proposed

#9 by Antti Karttunen at Sat Apr 26 14:16:43 EDT 2014

NAME

Characteristic function for A236841 (A234741): a(n) = 1, if n is a result of "downward" remultiplication (N -> GF(2)[X]) of some number, 0 otherwise.

#8 by Antti Karttunen at Mon Apr 14 13:05:04 EDT 2014

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 and , m < n that n = A048720(k,m) and a(k)*a(m) = 1, and 0 otherwise.

Discussion

Mon Apr 21

16:19

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#7 by Antti Karttunen at Mon Apr 14 13:01:25 EDT 2014

CROSSREFS

Positions of zeros occur in the same positions as in A236833; sequence A236834 gives these positions.

#6 by Antti Karttunen at Mon Apr 14 12:58:12 EDT 2014

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 are exists at least one such pair of k and m that n=A048720biA048720(k,m) and a(k)*a(m) = 1, 0 otherwise.

CROSSREFS

Positions of zeros occur in the same positions as in A236833.

Cf. A236841, A234741, A236862, A048720, A091225, A091255.

#5 by Antti Karttunen at Mon Apr 14 12:54:42 EDT 2014

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 if there are such k and m that n=A048720bi(k,m) and a(k)*a(m) = 1, 0 otherwise.

(Please compare also to the formula for A236862).

#4 by Antti Karttunen at Mon Apr 14 12:42:21 EDT 2014

LINKS

A. Karttunen, <a href="/A091247/a091247.scm.txt">Scheme-program, containing a few functions needed for computing this sequence.</a>

PROG

(Scheme, naive implementationtwo quite inefficient implementations, which require also definec and/or GF2Xdivide from a linked Scheme-source file)

(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

Cf. A236862, A091225, A091255.

#3 by Antti Karttunen at Mon Apr 14 12:35:54 EDT 2014

LINKS

Antti Karttunen, <a href="/A236861/b236861.txt">Table of n, a(n) for n = 0..8192</a>