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A286252 Compound filter: a(n) = P(A001511(1+n), A278222(n)), where P(n,k) is sequence A000027 used as a pairing function. 5
1, 5, 2, 18, 2, 23, 7, 59, 2, 23, 16, 94, 7, 80, 29, 195, 2, 23, 16, 94, 16, 467, 67, 355, 7, 80, 67, 706, 29, 302, 121, 672, 2, 23, 16, 94, 16, 467, 67, 355, 16, 467, 436, 1894, 67, 1832, 277, 1331, 7, 80, 67, 706, 67, 1832, 631, 2779, 29, 302, 277, 2704, 121, 1178, 497, 2422, 2, 23, 16, 94, 16, 467, 67, 355, 16, 467, 436, 1894, 67, 1832, 277, 1331, 16, 467, 436 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..16384

MathWorld, Pairing Function

FORMULA

a(n) = (1/2)*(2 + ((A001511(1+n)+A278222(n))^2) - A001511(1+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));

A286252(n) = (2 + ((A001511(1+n)+A278222(n))^2) - A001511(1+n) - 3*A278222(n))/2;

for(n=0, 16384, write("b286252.txt", n, " ", A286252(n)));

(Scheme) (define (A286252 n) (* (/ 1 2) (+ (expt (+ (A001511 (+ 1 n)) (A278222 n)) 2) (- (A001511 (+ 1 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 2 + bin(n - 1)[2:].count("1") - bin(n)[2:].count("1")

def a(n): return T(a001511(n + 1), a278222(n)) # Indranil Ghosh, May 07 2017

CROSSREFS

Cf. A000027, A001511, A278222, A286162, A286251, A286253, A286254.

Sequence in context: A246797 A087958 A286161 * A286154 A304635 A306198

Adjacent sequences:  A286249 A286250 A286251 * A286253 A286254 A286255

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 07 2017

STATUS

approved

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Last modified June 23 09:53 EDT 2021. Contains 345397 sequences. (Running on oeis4.)