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A153880
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Shift factorial base representation left by one digit.
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49
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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
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listen;
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internal format)
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OFFSET
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0,2
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COMMENTS
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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.
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LINKS
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FORMULA
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Other identities. For all n >= 0:
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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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)))))))
(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 a(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)))
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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STATUS
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approved
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