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
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
Crossrefs
Programs
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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
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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.
Comments