A153880 Shift factorial base representation left by one digit.

0, 2, 6, 8, 12, 14, 24, 26, 30, 32, 36, 38, 48, 50, 54, 56, 60, 62, 72, 74, 78, 80, 84, 86, 120, 122, 126, 128, 132, 134, 144, 146, 150, 152, 156, 158, 168, 170, 174, 176, 180, 182, 192, 194, 198, 200, 204, 206, 240, 242, 246, 248, 252, 254, 264, 266, 270, 272

Offset: 0

Author

Antti Karttunen, Jan 03 2009

Keywords

• base
• nonn

Comments

Equally, append 0 to the end of the factorial base representation of n (= A007623(n)), then convert back to decimal.

Involution A225901 maps each term of this sequence to a unique term of A255411, and vice versa.

Examples

			Factorial base representation of 5 is A007623(5) = "21". Shifting this once left (that is, appending 0 to the end) yields "210", which is factorial base representation for 14. Thus a(5) = 14.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 0..40319
• Index entries for sequences related to factorial base representation

Crossrefs

Indices of zeros in A260736.

Cf. A153883 (terms divided by 2).

Cf. A266193 (a left inverse).

Cf. A273670 (complement).

Cf. also A007623, A225901, A255411.

Programs

Mathematica

Table[Function[b, FromDigits[IntegerDigits[n, b]~Join~{0}, b]]@ MixedRadix[Reverse@ Range@ 12], {n, 0, 57}] (* Michael De Vlieger, May 30 2016, Version 10.2 *)

Python

from sympy import factorial as f
def a007623(n, p=2): return n if n
Indranil Ghosh, Jun 20 2017

Scheme

(define (A153880 n) (let loop ((n n) (z 0) (i 2) (f 2)) (cond ((zero? n) z) (else (loop (floor->exact (/ n i)) (+ (* f (modulo n i)) z) (+ 1 i) (* f (+ i 1)))))))

Formula

Other identities. For all n >= 0:

A266193(a(n)) = n.