A273663 - OEIS

%I #14 Mar 21 2021 13:00:20

%S 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 21,21,22,22,23,24,25,25,26,26,27,28,29,30,31,32,33,34,35,35,36,36,37,

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

%H Antti Karttunen, <a href="/A273663/b273663.txt">Table of n, a(n) for n = 1..10080</a>

%F a(1) = 0; for n > 1, a(n) = A257680(A225901(n)) + a(n-1).

%F Other identities.

%F For all n >= 0, a(A273670(n)) = n.

%o (Scheme, with memoization-macro definec)

%o (definec (A273663 n) (if (= 1 n) 0 (+ (A257680 (A225901 n)) (A273663 (- n 1)))))

%o (Python)

%o from sympy import factorial as f

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

%o def a225901(n):

%o     s=0

%o     k=2

%o     while n:

%o         d=n%k

%o         n=n//k

%o         if d: s=s+(k - d)*f(k - 1)

%o         k+=1

%o     return s

%o def a257680(n): return 1 if '1' in str(a007623(n)) else 0

%o def a(n): return 0 if n==1 else a257680(a225901(n)) + a(n - 1)

%o l=[0, 0]

%o for n in range(2, 101): l.append(a257680(a225901(n)) + l[n - 1])

%o print(l[1:]) # _Indranil Ghosh_, Jun 24 2017

%Y Left inverse of A273670.

%Y Cf. A225901, A257680.

%Y Cf. also A273662.

%K nonn

%O 1,4

%A _Antti Karttunen_, May 30 2016