

A273670


Numbers with at least one maximal digit in their factorial base representation.


40



1, 3, 4, 5, 7, 9, 10, 11, 13, 15, 16, 17, 18, 19, 20, 21, 22, 23, 25, 27, 28, 29, 31, 33, 34, 35, 37, 39, 40, 41, 42, 43, 44, 45, 46, 47, 49, 51, 52, 53, 55, 57, 58, 59, 61, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 75, 76, 77, 79, 81, 82, 83, 85, 87, 88, 89, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103, 104, 105
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OFFSET

0,2


COMMENTS

Indexing starts from 0 (with a(0) = 1) to tally with the indexing used in A256450.
Numbers n for which is A260736(n) > 0.
Involution A225901 maps each term of this sequence to a unique term of A256450, and vice versa.


LINKS



FORMULA

a(0) = 1, and for n > 1, if A260736(1+a(n1)) > 0, then a(n) = a(n1) + 1, otherwise a(n1) + 2. [In particular, if the previous term is 2k, then the next term is 2k+1, because all odd numbers are members.]
Other identities. For all n >= 0:


MATHEMATICA

r = MixedRadix[Reverse@ Range[2, 12]]; Select[Range@ 105, Total@ Boole@ Map[SameQ @@ # &, Transpose@{#, Range@ Length@ #}] > 0 &@ Reverse@ IntegerDigits[#, r] &] (* Michael De Vlieger, Aug 14 2016, Version 10.2 *)


PROG

;; Or as a naive recurrence with memoizationmacro definec:
(definec (A273670 n) (if (zero? n) 1 (let ((prev (A273670 ( n 1)))) (cond ((even? prev) (+ 1 prev)) ((not (zero? (A260736 (+ 1 prev)))) (+ 1 prev)) (else (+ 2 prev))))))
(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 a257684(n):
x=str(a007623(n))[:1]
y="".join([str(int(i)  1) if int(i)>0 else '0' for i in x])[::1]
return 0 if n==1 else sum([int(y[i])*f(i + 1) for i in range(len(y))])
def a260736(n): return 0 if n==0 else n%2 + a260736(a257684(n))
print([n for n in range(106) if a260736(n)>0]) # Indranil Ghosh, Jun 20 2017


CROSSREFS



KEYWORD

nonn,base


AUTHOR



STATUS

approved



