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A286462
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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.
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3
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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
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OFFSET
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1,3
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LINKS
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Antti Karttunen, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Pairing Function
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FORMULA
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a(n) = (1/2)*(2 + ((A051064(n)+A089309(n))^2) - A051064(n) - 3*A089309(n)).
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PROG
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(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
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CROSSREFS
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Cf. A000027, A051064, A089309, A286362, A286463, A286464.
Sequence in context: A323388 A260877 A237888 * A046607 A152717 A071856
Adjacent sequences: A286459 A286460 A286461 * A286463 A286464 A286465
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KEYWORD
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nonn
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AUTHOR
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Antti Karttunen, May 10 2017
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STATUS
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approved
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