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

Offset: 1

Author

Antti Karttunen, May 10 2017

Keywords

• nonn

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

Crossrefs

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

Programs

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)))

Formula

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