A286252 Compound filter: a(n) = P(A001511(1+n), A278222(n)), where P(n,k) is sequence A000027 used as a pairing function.

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

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 A367288 A304635

Adjacent sequences: A286249 A286250 A286251 * A286253 A286254 A286255

Keyword

nonn

Author

Antti Karttunen, May 07 2017

Status

approved