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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. 4
2, 2, 12, 2, 16, 12, 29, 2, 31, 16, 67, 12, 67, 29, 138, 2, 16, 31, 67, 16, 467, 67, 277, 12, 67, 67, 745, 29, 277, 138, 497, 2, 23, 16, 67, 31, 436, 67, 302, 16, 436, 467, 1771, 67, 1894, 277, 1129, 12, 67, 67, 668, 67, 1771, 745, 2557, 29, 302, 277, 2557, 138, 1129, 497, 2148, 2, 16, 23, 67, 16, 467, 67, 277, 31, 436, 436, 1832, 67, 1771, 302, 1129, 16, 566 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..10000

Indranil Ghosh, Python program to generate the sequence

Eric Weisstein's World of Mathematics, Pairing Function

FORMULA

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

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)));

(Scheme) (define (A286464 n) (* (/ 1 2) (+ (expt (+ (A051064 n) (A278222 n)) 2) (- (A051064 n)) (- (* 3 (A278222 n))) 2)))

CROSSREFS

Cf. A000027, A051064, A278222, A286462, A286463.

Sequence in context: A217094 A076976 A291757 * A058044 A223453 A285729

Adjacent sequences:  A286461 A286462 A286463 * A286465 A286466 A286467

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 10 2017

STATUS

approved

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Last modified May 15 01:43 EDT 2021. Contains 343909 sequences. (Running on oeis4.)