A257686 a(0) = 0, for n >= 1: a(n) = A099563(n) * A048764(n).

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

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(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 range(201)]) # Indranil Ghosh, Jun 21 2017

Crossrefs

Cf. A007623, A048764, A051683, A099563, A257687.

Cf. also A053644 (analogous sequence for base-2).

Sequence in context: A347661 A007730 A330271 * A057144 A198332 A080606

Adjacent sequences: A257683 A257684 A257685 * A257687 A257688 A257689

Keyword

nonn,base

Author

Antti Karttunen, May 04 2015

Status

approved