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 A153880 Shift factorial base representation left by one digit. 47
 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 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 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. LINKS Antti Karttunen, Table of n, a(n) for n = 0..40319 FORMULA Other identities. For all n >= 0: A266193(a(n)) = n. EXAMPLE 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. 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 *) PROG (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))))))) (Python) from sympy import factorial as f def a007623(n, p=2): return n if n

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Last modified July 25 19:05 EDT 2021. Contains 346291 sequences. (Running on oeis4.)