cp's OEIS Frontend

A273670 Numbers with at least one maximal digit in their factorial base representation.

%I A273670 #25 Apr 30 2020 13:35:47
%S A273670 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,
%T A273670 35,37,39,40,41,42,43,44,45,46,47,49,51,52,53,55,57,58,59,61,63,64,65,
%U A273670 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
%N A273670 Numbers with at least one maximal digit in their factorial base representation.
%C A273670 Indexing starts from 0 (with a(0) = 1) to tally with the indexing used in A256450.
%C A273670 Numbers n for which is A260736(n) > 0.
%C A273670 Involution A225901 maps each term of this sequence to a unique term of A256450, and vice versa.
%H A273670 Antti Karttunen, <a href="/A273670/b273670.txt">Table of n, a(n) for n = 0..10000</a>
%H A273670 <a href="/index/Fa#facbase">Index entries for sequences related to factorial base representation</a>
%F A273670 a(0) = 1, and for n > 1, if A260736(1+a(n-1)) > 0, then a(n) = a(n-1) + 1, otherwise a(n-1) + 2. [In particular, if the previous term is 2k, then the next term is 2k+1, because all odd numbers are members.]
%F A273670 Other identities. For all n >= 0:
%F A273670 A273663(a(n)) = n.
%t A273670 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 *)
%o A273670 (Scheme, with _Antti Karttunen_'s IntSeq-library)
%o A273670 (define A273670 (NONZERO-POS 0 0 A260736))
%o A273670 ;; Or as a naive recurrence with memoization-macro definec:
%o A273670 (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))))))
%o A273670 (Python)
%o A273670 from sympy import factorial as f
%o A273670 def a007623(n, p=2): return n if n<p else a007623(int(n/p), p+1)*10 + n%p
%o A273670 def a257684(n):
%o A273670     x=str(a007623(n))[:-1]
%o A273670     y="".join([str(int(i) - 1) if int(i)>0 else '0' for i in x])[::-1]
%o A273670     return 0 if n==1 else sum([int(y[i])*f(i + 1) for i in range(len(y))])
%o A273670 def a260736(n): return 0 if n==0 else n%2 + a260736(a257684(n))
%o A273670 print([n for n in range(106) if a260736(n)>0]) # _Indranil Ghosh_, Jun 20 2017
%Y A273670 Cf. A153880 (complement).
%Y A273670 Cf. A273663 (a left inverse).
%Y A273670 Cf. A260736.
%Y A273670 Cf. also A225901, A256450.
%K A273670 nonn,base
%O A273670 0,2
%A A273670 _Antti Karttunen_, May 29 2016