A275959 Sum of distinct terms of A002674: a(0) = 0, a(2n) = A255411(A153880(a(n))), a(2n+1) = 1+A255411(A153880(a(n))).

0, 1, 12, 13, 360, 361, 372, 373, 20160, 20161, 20172, 20173, 20520, 20521, 20532, 20533, 1814400, 1814401, 1814412, 1814413, 1814760, 1814761, 1814772, 1814773, 1834560, 1834561, 1834572, 1834573, 1834920, 1834921, 1834932, 1834933, 239500800, 239500801, 239500812, 239500813, 239501160, 239501161, 239501172, 239501173, 239520960, 239520961

Offset

0,3

Comments

Fixed points of involution A225901.

This can be also viewed as a function that reinterprets base-2 representation of n in base-((2n)!/2) where the digits are multiplied with the successive terms of A002674, thus a(0) = 0.

Links

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

Index entries for sequences related to factorial base representation

Formula

a(0) = 0, a(2n) = A255411(A153880(a(n))), a(2n+1) = 1+A255411(A153880(a(n))).

a(n) = A276089(A276091(n)).

Prog

(Scheme, three versions. Some require Antti Karttunen's IntSeq-library)
;; This implements the given recurrence:
(definec (A275959 n) (cond ((zero? n) n) ((even? n) (A255411 (A153880 (A275959 (/ n 2))))) (else (+ 1 (A255411 (A153880 (A275959 (/ (- n 1) 2))))))))
(define (A275959 n) (A276089 (A276091 n)))
(define A275959 (FIXED-POINTS 0 0 A225901)) ;; Slow!
(Python)
from sympy import factorial as f
def a007623(n, p=2): return n if n<p else a007623(n//p, p+1)*10 + n%p
def a255411(n):
    x=(str(a007623(n)) + '0')
    y="".join(str(int(i) + 1) if int(i)>0 else '0' for i in x)[::-1]
    return 0 if n==0 else sum([int(y[i])*f(i + 1) for i in range(len(y))])
def a153880(n):
    x=(str(a007623(n)) + '0')[::-1]
    return 0 if n==0 else sum([int(x[i])*f(i + 1) for i in range(len(x))])
def a(n): return 0 if n==0 else a255411(a153880(a(n//2))) if n%2==0 else 1 + a255411(a153880(a((n - 1)//2)))
print([a(n) for n in range(101)]) # Indranil Ghosh, Jun 20 2017

Crossrefs

Cf. A002674, A059590, A153880, A255411, A276082, A276083, A276091.

Fixed points of A225901.

Subsequence of A275956 and of A276089.

Sequence in context: A260387 A041309 A041310 * A066321 A099415 A042293

Adjacent sequences: A275956 A275957 A275958 * A275960 A275961 A275962

Keyword

nonn,base

Author

Antti Karttunen, Aug 16 2016

Status

approved