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A264990 a(n) = number of occurrences of a most frequent nonzero digit in factorial base representation (A007623) of n. 9
0, 1, 1, 2, 1, 1, 1, 2, 2, 3, 1, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 3, 1, 2, 2, 3, 3, 4, 2, 3, 1, 2, 2, 3, 2, 2, 1, 2, 2, 3, 1, 2, 1, 1, 1, 2, 2, 2, 1, 2, 2, 3, 2, 2, 2, 2, 2, 2, 3, 3, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 3, 1, 2, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2, 2, 3, 1, 2, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 1, 1, 1, 2 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

Antti Karttunen, Table of n, a(n) for n = 0..10080

Index entries for sequences related to factorial base representation

FORMULA

a(0) = 0; for n >= 1, a(n) = max(A257511(n), a(A257684(n)).

Other identities. For all n >= 0:

From Antti Karttunen, Aug 15 2016: (Start)

a(n) = A275811(A225901(n)).

a(n) = A051903(A275735(n)).

(End)

EXAMPLE

   n  A007623(n)   a(n) [highest number of times any nonzero digit occurs].

   0 =   0           0 (because no nonzero digits present)

   1 =   1           1

   2 =  10           1

   3 =  11           2

   4 =  20           1

   5 =  21           1

   6 = 100           1

   7 = 101           2

   8 = 110           2

   9 = 111           3

  10 = 120           1

  11 = 121           2

  12 = 200           1

  13 = 201           1

  14 = 210           1

  15 = 211           2

  16 = 220           2

  17 = 221           2

  18 = 300           1

and for n=63 we have:

  63 = 2211          2.

PROG

(Scheme with memoization-macro definec)

(definec (A264990 n) (if (zero? n) n (max (A257511 n) (A264990 (A257684 n)))))

(Python)

from sympy import prime, factorint

from operator import mul

import collections

def a007623(n, p=2): return n if n<p else a007623(int(n/p), p+1)*10 + n%p

def a051903(n): return 0 if n==1 else max(factorint(n).values())

def a275735(n):

    y=collections.Counter(map(int, list(str(a007623(n)).replace("0", "")))).most_common()

    return 1 if n==0 else reduce(mul, [prime(y[i][0])**y[i][1] for i in xrange(len(y))])

def a(n): return 0 if n==0 else a051903(a275735(n))

print [a(n) for n in xrange(201)] # Indranil Ghosh, Jun 20 2017

CROSSREFS

Cf. A007623, A051903, A225901, A257511, A257684, A275735, A275811.

Cf. A265349 (positions of terms <= 1), A265350 (positions of term > 1).

Cf. also A266117, A266118.

Sequence in context: A110730 A198339 A262561 * A277315 A277326 A050431

Adjacent sequences:  A264987 A264988 A264989 * A264991 A264992 A264993

KEYWORD

nonn,base

AUTHOR

Antti Karttunen, Dec 22 2015

EXTENSIONS

Name changed by Antti Karttunen, Aug 15 2016

STATUS

approved

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Last modified November 20 02:34 EST 2019. Contains 329323 sequences. (Running on oeis4.)