A286464 - OEIS

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.

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