A277021 Left inverse of A277022.

0, 1, 2, 2, 6, 3, 4, 3, 30, 7, 8, 4, 12, 5, 6, 4, 210, 31, 32, 8, 36, 9, 10, 5, 60, 13, 14, 6, 18, 7, 8, 5, 2310, 211, 212, 32, 216, 33, 34, 9, 240, 37, 38, 10, 42, 11, 12, 6, 420, 61, 62, 14, 66, 15, 16, 7, 90, 19, 20, 8, 24, 9, 10, 6, 30030, 2311, 2312, 212, 2316, 213, 214, 33, 2340, 217, 218, 34, 222, 35, 36, 10, 2520, 241, 242

Offset

0,3

Links

Antti Karttunen, Table of n, a(n) for n = 0..8191

Index entries for sequences related to binary expansion of n

Index entries for sequences related to primorial base

Formula

a(n) = A276085(A005940(1+n)).

Other identities. For all n >= 0:

a(A277022(n)) = n.

Prog

(Scheme)
(define (A277021 n) (let loop ((s 0) (n n) (r 0) (i 1) (pr 1)) (cond ((zero? n) (+ s (* r pr))) ((even? n) (loop (+ s (* r pr)) (/ n 2) 0 (+ 1 i) (* (A000040 i) pr))) (else (loop s (/ (- n 1) 2) (+ 1 r) i pr)))))
(Python)
from sympy import primorial, primepi, prime, factorint, floor, log
def a002110(n): return 1 if n<1 else primorial(n)
def a276085(n):
    f=factorint(n)
    return sum([f[i]*a002110(primepi(i) - 1) for i in f])
def A(n): return n - 2**int(floor(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 a(n): return a276085(b(n - 1))
print([a(n) for n in range(1, 101)]) # Indranil Ghosh, Jun 22 2017

Crossrefs

Left inverse of A277022.

Cf. A005940, A276085.

Cf. also A277017.

Sequence in context: A128623 A182701 A277011 * A275037 A174833 A085738

Adjacent sequences: A277018 A277019 A277020 * A277022 A277023 A277024

Keyword

nonn,base

Author

Antti Karttunen, Sep 26 2016

Status

approved