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A286162 Compound filter: a(n) = T(A001511(n), A278222(n)), where T(n,k) is sequence A000027 used as a pairing function. 16
2, 5, 7, 9, 16, 12, 29, 14, 16, 23, 67, 18, 67, 38, 121, 20, 16, 23, 67, 31, 436, 80, 277, 25, 67, 80, 631, 48, 277, 138, 497, 27, 16, 23, 67, 31, 436, 80, 277, 40, 436, 467, 1771, 94, 1771, 302, 1129, 33, 67, 80, 631, 94, 1771, 668, 2557, 59, 277, 302, 2557, 156, 1129, 530, 2017, 35, 16, 23, 67, 31, 436, 80, 277, 40, 436, 467, 1771, 94, 1771, 302, 1129, 50 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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 + ((A001511(n)+A278222(n))^2) - A001511(n) - 3*A278222(n)).

PROG

(PARI)

A001511(n) = (1+valuation(n, 2));

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

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));

A286162(n) = (2 + ((A001511(n)+A278222(n))^2) - A001511(n) - 3*A278222(n))/2;

for(n=1, 10000, write("b286162.txt", n, " ", A286162(n)));

(Scheme) (define (A286162 n) (* (/ 1 2) (+ (expt (+ (A001511 n) (A278222 n)) 2) (- (A001511 n)) (- (* 3 (A278222 n))) 2)))

(Python)

from sympy import prime, factorint

import math

def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2

def A(n): return n - 2**int(math.floor(math.log(n, 2)))

def b(n): return n + 1 if n<2 else prime(1 + (len(bin(n)[2:]) - bin(n)[2:].count("1"))) * b(A(n))

def a005940(n): return b(n - 1)

def P(n):

    f = factorint(n)

    return sorted([f[i] for i in f])

def a046523(n):

    x=1

    while True:

        if P(n) == P(x): return x

        else: x+=1

def a278222(n): return a046523(a005940(n + 1))

def a001511(n): return bin(n)[2:][::-1].index("1") + 1

def a(n): return T(a001511(n), a278222(n)) # Indranil Ghosh, May 05 2017

CROSSREFS

Cf. A000027, A001511, A278222, A286160, A286161, A286163, A286164.

Sequence in context: A287363 A253275 A093417 * A286164 A211167 A083272

Adjacent sequences:  A286159 A286160 A286161 * A286163 A286164 A286165

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 04 2017

STATUS

approved

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Last modified January 18 13:30 EST 2020. Contains 331007 sequences. (Running on oeis4.)