login
This site is supported by donations to The OEIS Foundation.

 

Logo


Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A286241 Compound filter: a(n) = P(A278219(n), A278219(1+n)), where P(n,k) is sequence A000027 used as a pairing function. 3
2, 12, 14, 12, 59, 86, 27, 12, 109, 363, 269, 86, 142, 148, 27, 12, 109, 1093, 1117, 363, 1097, 1517, 489, 86, 601, 1408, 619, 148, 142, 148, 27, 12, 109, 1093, 1117, 1093, 5707, 8587, 2545, 363, 1969, 6153, 4529, 1517, 4489, 4537, 489, 86, 601, 3946, 3976, 1408, 2509, 5719, 2545, 148, 601, 1408, 619, 148, 142, 148, 27, 12, 109, 1093, 1117, 1093, 5707, 8587 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,1

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..16383

Eric Weisstein's World of Mathematics, Pairing Function

FORMULA

a(n) = (1/2)*(2+((A278219(n)+A278219(1+n))^2) - A278219(n) - 3*A278219(1+n)).

MATHEMATICA

f[n_, i_, x_] := Which[n == 0, x, EvenQ@ n, f[n/2, i + 1, x], True, f[(n - 1)/2, i, x Prime@ i]]; g[n_] := If[n == 1, 1, Times @@ MapIndexed[ Prime[First@ #2]^#1 &, Sort[FactorInteger[n][[All, -1]], Greater]]]; h[n_] := g@ f[BitXor[n, Floor[n/2]], 1, 1]; Map[(2 + (#1 + #2)^2 - #1 - 3 #2)/2 & @@ # & /@ # &, Table[{h[n], h[n + 1]}, {k, 12}, {n, k (k - 1)/2, k (k + 1)/2 - 1}]] // Flatten (* Michael De Vlieger, May 09 2017 *)

PROG

(PARI)

A003188(n) = bitxor(n, n>>1);

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));

A278219(n) = A278222(A003188(n));

A286241(n) = (2 + ((A278219(n)+A278219(1+n))^2) - A278219(n) - 3*A278219(1+n))/2;

for(n=0, 16383, write("b286241.txt", n, " ", A286241(n)));

(Scheme) (define (A286241 n) (* (/ 1 2) (+ (expt (+ (A278219 n) (A278219 (+ 1 n))) 2) (- (A278219 n)) (- (* 3 (A278219 (+ 1 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 a003188(n): return n^int(n/2)

def a243353(n): return a005940(1 + a003188(n))

def a278219(n): return a046523(a243353(n))

def a(n): return T(a278219(n), a278219(n + 1)) # Indranil Ghosh, May 07 2017

CROSSREFS

Cf. A000027, A003188, A005940, A046523, A243353, A278219, A278222, A286240, A286242, A286255.

Sequence in context: A141273 A010097 A103761 * A078755 A186647 A086285

Adjacent sequences:  A286238 A286239 A286240 * A286242 A286243 A286244

KEYWORD

nonn

AUTHOR

Antti Karttunen, May 07 2017

STATUS

approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified October 23 23:51 EDT 2019. Contains 328379 sequences. (Running on oeis4.)