A236861 - OEIS

The OEIS is supported by the many generous donors to the OEIS Foundation.

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Other ways to Give

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.

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

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..8192

A. Karttunen, Scheme-program, containing a few functions needed for computing this sequence.

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: A015343 A296077 A322674 * A016300 A016126 A016068

Adjacent sequences: A236858 A236859 A236860 * A236862 A236863 A236864

KEYWORD

nonn

AUTHOR

Antti Karttunen, Apr 13 2014

STATUS

approved