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A273663 Least monotonic left inverse for A273670: a(1) = 0; for n > 1, a(n) = A257680(A225901(n)) + a(n-1).

%I A273663 #14 Mar 21 2021 13:00:20
%S A273663 0,0,1,2,3,3,4,4,5,6,7,7,8,8,9,10,11,12,13,14,15,16,17,17,18,18,19,20,
%T A273663 21,21,22,22,23,24,25,25,26,26,27,28,29,30,31,32,33,34,35,35,36,36,37,
%U A273663 38,39,39,40,40,41,42,43,43,44,44,45,46,47,48,49,50,51,52,53,53,54,54,55,56,57,57,58,58,59,60,61,61
%N A273663 Least monotonic left inverse for A273670: a(1) = 0; for n > 1, a(n) = A257680(A225901(n)) + a(n-1).
%H A273663 Antti Karttunen, <a href="/A273663/b273663.txt">Table of n, a(n) for n = 1..10080</a>
%F A273663 a(1) = 0; for n > 1, a(n) = A257680(A225901(n)) + a(n-1).
%F A273663 Other identities.
%F A273663 For all n >= 0, a(A273670(n)) = n.
%o A273663 (Scheme, with memoization-macro definec)
%o A273663 (definec (A273663 n) (if (= 1 n) 0 (+ (A257680 (A225901 n)) (A273663 (- n 1)))))
%o A273663 (Python)
%o A273663 from sympy import factorial as f
%o A273663 def a007623(n, p=2): return n if n<p else a007623(n//p, p+1)*10 + n%p
%o A273663 def a225901(n):
%o A273663     s=0
%o A273663     k=2
%o A273663     while n:
%o A273663         d=n%k
%o A273663         n=n//k
%o A273663         if d: s=s+(k - d)*f(k - 1)
%o A273663         k+=1
%o A273663     return s
%o A273663 def a257680(n): return 1 if '1' in str(a007623(n)) else 0
%o A273663 def a(n): return 0 if n==1 else a257680(a225901(n)) + a(n - 1)
%o A273663 l=[0, 0]
%o A273663 for n in range(2, 101): l.append(a257680(a225901(n)) + l[n - 1])
%o A273663 print(l[1:]) # _Indranil Ghosh_, Jun 24 2017
%Y A273663 Left inverse of A273670.
%Y A273663 Cf. A225901, A257680.
%Y A273663 Cf. also A273662.
%K A273663 nonn
%O A273663 1,4
%A A273663 _Antti Karttunen_, May 30 2016