A286462 Compound filter (3-adic valuation & the length of rightmost run of 1's in base-2): a(n) = P(A051064(n), A089309(n)), where P(n,k) is sequence A000027 used as a pairing function.

1, 1, 5, 1, 1, 5, 4, 1, 6, 1, 2, 5, 1, 4, 12, 1, 1, 6, 2, 1, 3, 2, 4, 5, 1, 1, 14, 4, 1, 12, 11, 1, 3, 1, 2, 6, 1, 2, 8, 1, 1, 3, 2, 2, 6, 4, 7, 5, 1, 1, 5, 1, 1, 14, 4, 4, 3, 1, 2, 12, 1, 11, 31, 1, 1, 3, 2, 1, 3, 2, 4, 6, 1, 1, 5, 2, 1, 8, 7, 1, 15, 1, 2, 3, 1, 2, 8, 2, 1, 6, 2, 4, 3, 7, 11, 5, 1, 1, 9, 1, 1, 5, 4, 1, 3, 1, 2, 14, 1, 4, 12, 4, 1, 3, 2, 1

Offset

1,3

Links

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

Eric Weisstein's World of Mathematics, Pairing Function

Formula

a(n) = (1/2)*(2 + ((A051064(n)+A089309(n))^2) - A051064(n) - 3*A089309(n)).

Prog

(PARI)
A051064(n) = if(n<1, 0, 1+valuation(n, 3));
A089309(n) = valuation((n/2^valuation(n, 2))+1, 2); \\ After Ralf Stephan
A286462(n) = (1/2)*(2 + ((A051064(n)+A089309(n))^2) - A051064(n) - 3*A089309(n));
for(n=1, 10000, write("b286462.txt", n, " ", A286462(n)));
(Scheme) (define (A286462 n) (* (/ 1 2) (+ (expt (+ (A051064 n) (A089309 n)) 2) (- (A051064 n)) (- (* 3 (A089309 n))) 2)))
(Python)
from sympy import divisors, divisor_count, mobius
def a051064(n): return -sum([mobius(3*d)*divisor_count(n/d) for d in divisors(n)])
def v(n): return bin(n)[2:][::-1].index("1")
def a089309(n): return  0 if n==0 else v(n/2**v(n) + 1)
def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2
def a(n): return T(a051064(n), a089309(n)) # Indranil Ghosh, May 11 2017

Crossrefs

Cf. A000027, A051064, A089309, A286362, A286463, A286464.

Sequence in context: A260877 A353305 A237888 * A046607 A152717 A071856

Adjacent sequences: A286459 A286460 A286461 * A286463 A286464 A286465

Keyword

nonn

Author

Antti Karttunen, May 10 2017

Status

approved