The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A361128 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A361128

Let b = A360519; let Lg = gcd(b(n-1),b(n)), Rg = gcd(b(n),b(n+1)); let L(n) = prod_{primes p|Lg} p-part of b(n), R(n) = prod_{primes p|Rg} p-part of b(n), M(n) = b(n)/(L(n)*R(n)); sequence gives L(n).
(history; published version)

#34 by N. J. A. Sloane at Fri Mar 10 07:48:52 EST 2023

STATUS

editing

approved

#33 by N. J. A. Sloane at Fri Mar 10 07:48:50 EST 2023

COMMENTS

One can think of A360519 as a chain of circles, each circle linked to its neighbors to the left and the right. The n-th terms term b(n) = A360519(n) is a product a(n) = L(n)*M(n)*R(n), where L(n) is the part of ab(n) sharing primes with the term to the left, R(n) the part sharing primes with the term to the right, and M(n) is the rest of ab(n).

By definition of the sequence A360519, the set of primes in L(n) are is disjoint from the primes in R(n).

STATUS

approved

editing

#32 by N. J. A. Sloane at Fri Mar 10 00:45:29 EST 2023

STATUS

editing

approved

#31 by N. J. A. Sloane at Fri Mar 10 00:45:25 EST 2023

COMMENTS

One can think of A360519 as a chain of circles, each circle linked to its neighbors to the left and the right. The n-th terms is a product a(n) = L(n)*M(n)*R(n), where L(n) is the part of a(n) sharing primes with the term to the left, R(n) the part sharing primes with the term to the right, and M(n) is the rest of a(n).

By definition of the sequence A360519, the primes in L(n) are disjoint from the primes in R(n).

STATUS

approved

editing

#30 by N. J. A. Sloane at Thu Mar 09 18:55:31 EST 2023

STATUS

editing

approved

#29 by N. J. A. Sloane at Thu Mar 09 18:55:29 EST 2023

MAPLE

with(numtheory);

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approved

editing

#28 by N. J. A. Sloane at Thu Mar 09 18:53:00 EST 2023

STATUS

editing

approved

#27 by N. J. A. Sloane at Thu Mar 09 18:52:57 EST 2023

MAPLE

# Then f3(bW[n-1], bW[n], bW[n+1]); returns [L(n), M(n), R(n)) ] where:

STATUS

approved

editing

#26 by N. J. A. Sloane at Thu Mar 09 18:52:00 EST 2023

STATUS

editing

approved

#25 by N. J. A. Sloane at Thu Mar 09 18:51:56 EST 2023

MAPLE

end; # _N. J. A. Sloane_, Mar 09 2023

STATUS

approved

editing