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A273662 Least monotonic left inverse for A256450: a(1) = 0; for n > 1, a(n) = A257680(n) + a(n-1).

%I A273662 #18 Mar 09 2021 19:14:07
%S A273662 0,1,2,2,3,4,5,6,7,8,9,9,10,11,12,12,13,13,14,15,16,16,17,18,19,20,21,
%T A273662 22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,41,42,43,
%U A273662 44,44,45,46,47,48,49,50,51,51,52,53,54,54,55,55,56,57,58,58,59,59,60,61,62,62,63,64,65,66,67,68,69,69,70
%N A273662 Least monotonic left inverse for A256450: a(1) = 0; for n > 1, a(n) = A257680(n) + a(n-1).
%C A273662 Partial sums of A257680 from term A257680(2) onward.
%H A273662 Antti Karttunen, <a href="/A273662/b273662.txt">Table of n, a(n) for n = 1..10080</a>
%F A273662 a(1) = 0; for n > 1, a(n) = A257680(n) + a(n-1).
%F A273662 Other identities.
%F A273662 For all n >= 1, a(n) = A257682(n)-1.
%F A273662 For all n >= 0, a(A256450(n)) = n. [This sequence works as a left inverse of A256450.]
%o A273662 (Scheme, with memoization-macro definec)
%o A273662 (definec (A273662 n) (if (= 1 n) 0 (+ (A257680 n) (A273662 (- n 1)))))
%o A273662 (define (A273662 n) (- (A257682 n) 1))
%o A273662 (Python)
%o A273662 def a007623(n, p=2): return n if n<p else a007623(n//p, p+1)*10 + n%p
%o A273662 def a257680(n): return 1 if '1' in str(a007623(n)) else 0
%o A273662 l=[0, 0]
%o A273662 for n in range(2, 101):
%o A273662     l.append(a257680(n) + l[n - 1])
%o A273662 print(l[1:]) # _Indranil Ghosh_, Jun 24 2017
%Y A273662 One less than A257682.
%Y A273662 Cf. A256450, A257680.
%Y A273662 Cf. also A273663.
%K A273662 nonn
%O A273662 1,3
%A A273662 _Antti Karttunen_, May 29 2016