The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A286464

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A286464

Compound filter (3-adic valuation & signature for base-2 1-runs): a(n) = P(A051064(n), A278222(n)), where P(n,k) is sequence A000027 used as a pairing function.
(history; published version)

#12 by Bruno Berselli at Fri May 12 03:33:00 EDT 2017

STATUS

proposed

approved

#11 by Michel Marcus at Thu May 11 14:19:33 EDT 2017

STATUS

editing

proposed

#10 by Michel Marcus at Thu May 11 14:19:27 EDT 2017

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a>

STATUS

proposed

editing

#9 by Indranil Ghosh at Thu May 11 12:00:02 EDT 2017

STATUS

editing

proposed

#8 by Indranil Ghosh at Thu May 11 11:59:25 EDT 2017

LINKS

Indranil Ghosh, <a href="/A286464/a286464.txt">Python program to generate the sequence</a>

STATUS

approved

editing

#7 by N. J. A. Sloane at Wed May 10 17:47:07 EDT 2017

STATUS

proposed

approved

#6 by Antti Karttunen at Wed May 10 14:52:06 EDT 2017

STATUS

editing

proposed

#5 by Antti Karttunen at Wed May 10 13:02:03 EDT 2017

NAME

Compound filter (3-adic valuation & binary signature for base-2 1-runs): a(n) = P(A051064(n), A278222(n)), where P(n,k) is sequence A000027 used as a pairing function.

LINKS

Antti Karttunen, <a href="/A286464/b286464.txt">Table of n, a(n) for n = 1..10000</a>

PROG

(PARI)

A005940(n) = { my(p=2, t=1); n--; until(!n\=2, if((n%2), (t*=p), p=nextprime(p+1))); t }; \\ Modified from code of M. F. Hasler

A051064(n) = if(n<1, 0, 1+valuation(n, 3));

A046523(n) = { my(f=vecsort(factor(n)[, 2], , 4), p); prod(i=1, #f, (p=nextprime(p+1))^f[i]); }; \\ This function from Charles R Greathouse IV, Aug 17 2011

A278222(n) = A046523(A005940(1+n));

A286464(n) = (1/2)*(2 + ((A051064(n)+A278222(n))^2) - A051064(n) - 3*A278222(n))

for(n=1, 10000, write("b286464.txt", n, " ", A286464(n)));

Discussion

Wed May 10

14:52

Antti Karttunen: Used as a filtering sequence, thus a longish data section.

#4 by Antti Karttunen at Wed May 10 12:57:08 EDT 2017

NAME

Compound filter (3-adic valuation & binary 1-runs signature for 1-runs): a(n) = P(A051064(n), A278222(n)), where P(n,k) is sequence A000027 used as a pairing function.

LINKS

Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/PairingFunction.html">Pairing Function</a>

#3 by Antti Karttunen at Wed May 10 11:35:54 EDT 2017

NAME

Compound filter (3-adic valuation & binary 1-runs signature): a(n) = P(A051064(n), A278222(n)), where P(n,k) is sequence A000027 used as a pairing function.