A286255 Compound filter: a(n) = P(A046523(n), A046523(1+n)), where P(n,k) is sequence A000027 used as a pairing function.

2, 5, 12, 14, 23, 27, 38, 63, 40, 27, 80, 90, 23, 61, 216, 152, 80, 90, 80, 148, 61, 27, 302, 375, 40, 84, 179, 90, 467, 495, 530, 698, 61, 61, 826, 702, 23, 61, 412, 324, 467, 495, 80, 265, 148, 27, 1178, 1323, 109, 148, 142, 90, 302, 430, 412, 430, 61, 27, 1832, 1890, 23, 142, 2787, 2410, 601, 495, 80, 148, 601, 495, 2630, 2700, 23, 142, 265, 148, 601, 495, 1178

Offset

1,1

Links

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

MathWorld, Pairing Function

Formula

a(n) = (1/2)*(2 + ((A046523(n)+A046523(1+n))^2) - A046523(n) - 3*A046523(1+n)).

Prog

(PARI)
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
A286255(n) = (2 + ((A046523(n)+A046523(1+n))^2) - A046523(n) - 3*A046523(1+n))/2;
for(n=1, 10000, write("b286255.txt", n, " ", A286255(n)));
(Scheme) (define (A286255 n) (* (/ 1 2) (+ (expt (+ (A046523 n) (A046523 (+ 1 n))) 2) (- (A046523 n)) (- (* 3 (A046523 (+ 1 n)))) 2)))
(Python)
from sympy import factorint
def T(n, m): return ((n + m)**2 - n - 3*m + 2)/2
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 a(n): return T(a046523(n), a046523(n + 1)) # Indranil Ghosh, May 07 2017

Crossrefs

Cf. A000027, A046523, A286240, A286256, A286257, A286258.

Cf. A005383 (after its initial term 3, gives the positions of 23's in this sequence).

Cf. A051950 (one of the matches not matched by A046523 alone).

Sequence in context: A039586 A352785 A114217 * A286160 A286163 A286240

Adjacent sequences: A286252 A286253 A286254 * A286256 A286257 A286258

Keyword

nonn

Author

Antti Karttunen, May 07 2017

Status

approved