A286259 Compound filter: a(n) = P(A001511(n), A049820(n)), where P(n,k) is sequence A000027 used as a pairing function.

1, 2, 1, 6, 4, 5, 11, 25, 16, 23, 37, 31, 56, 57, 56, 110, 106, 80, 137, 123, 137, 173, 211, 175, 232, 255, 254, 279, 352, 255, 407, 471, 407, 467, 466, 409, 596, 597, 596, 599, 742, 597, 821, 783, 742, 905, 991, 866, 1036, 992, 1082, 1131, 1276, 1083, 1276, 1279, 1379, 1487, 1597, 1228, 1712, 1713, 1597, 1960, 1831, 1713, 2081, 2019, 2081, 1955, 2347, 1957

Offset

1,2

Links

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

MathWorld, Pairing Function

Formula

a(n) = (1/2)*(2 + ((A001511(n)+A049820(n))^2) - A001511(n) - 3*A049820(n)).

Prog

(PARI)
A001511(n) = (1+valuation(n, 2));
A049820(n) = (n-numdiv(n));
A286259(n) = (2 + ((A001511(n)+A049820(n))^2) - A001511(n) - 3*A049820(n))/2;
for(n=1, 10000, write("b286259.txt", n, " ", A286259(n)));
(Scheme) (define (A286259 n) (* (/ 1 2) (+ (expt (+ (A001511 n) (A049820 n)) 2) (- (A001511 n)) (- (* 3 (A049820 n))) 2)))
(Python)
from sympy import divisor_count as d
def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2
def a001511(n): return 2 + bin(n - 1)[2:].count("1") - bin(n)[2:].count("1")
def a(n): return T(a001511(n), n - d(n)) # Indranil Ghosh, May 07 2017

Crossrefs

Cf. A000027, A001511, A049820, A286161, A286162, A286260, A286034.

Sequence in context: A098697 A193094 A021466 * A257134 A121403 A155550

Adjacent sequences: A286256 A286257 A286258 * A286260 A286261 A286262

Keyword

nonn

Author

Antti Karttunen, May 07 2017

Status

approved