



0, 1, 2, 2, 4, 4, 6, 6, 6, 6, 6, 6, 12, 12, 12, 12, 12, 12, 18, 18, 18, 18, 18, 18, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 24, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 48, 72
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OFFSET

0,3


COMMENTS

For n >= 1, a(n) = the smallest term of A051683 >= n.
Can also be obtained by replacing with zeros all other digits except the first (the most significant) in the factorial base representation of n (A007623), then converting back to decimal.
Useful when computing A257687.


LINKS

Antti Karttunen, Table of n, a(n) for n = 0..5040


FORMULA

a(0) = 0, and for n >= 1: a(n) = A099563(n) * A048764(n).
Other identities:
For all n >= 0, a(n) = n  A257687(n).
a(n) = A000030(A007623(n))*(A055642(A007623(n)))!  Indranil Ghosh, Jun 21 2017


EXAMPLE

Factorial base representation (A007623) of 2 is "10", zeroing all except the most significant digit does not change anything, thus a(2) = 2.
Factorial base representation (A007623) of 3 is "11", zeroing all except the most significant digit gives "10", thus a(3) = 2.
Factorial base representation of 23 is "321", zeroing all except the most significant digit gives "300" which is factorial base representation of 18, thus a(23) = 18.


PROG

(Scheme) (define (A257686 n) (if (zero? n) n (* (A099563 n) (A048764 n))))
(Python)
from sympy import factorial as f
def a007623(n, p=2): return n if n<p else a007623(int(n/p), p+1)*10 + n%p
def a(n):
x=str(a007623(n))
return int(x[0])*f(len(x))
print [a(n) for n in xrange(201)] # Indranil Ghosh, Jun 21 2017


CROSSREFS

Cf. A007623, A048764, A051683, A099563, A257687.
Cf. also A053644 (analogous sequence for base2).
Sequence in context: A109874 A069345 A007730 * A057144 A198332 A080606
Adjacent sequences: A257683 A257684 A257685 * A257687 A257688 A257689


KEYWORD

nonn,base


AUTHOR

Antti Karttunen, May 04 2015


STATUS

approved



