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a(n) = the least k such that A131205(1+k) >= n; each n occurs A000123(n) times.
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%I #9 Nov 16 2016 11:08:54

%S 0,1,1,2,2,2,2,3,3,3,3,3,3,4,4,4,4,4,4,4,4,4,4,5,5,5,5,5,5,5,5,5,5,5,

%T 5,5,5,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,6,7,7,7,7,7,7,7,7,7,7,7,

%U 7,7,7,7,7,7,7,7,7,7,7,7,7,7,7,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8,8

%N a(n) = the least k such that A131205(1+k) >= n; each n occurs A000123(n) times.

%C Greatest monotonic left inverse of A131205(1+n).

%H Antti Karttunen, <a href="/A278163/b278163.txt">Table of n, a(n) for n = 1..9669</a>

%F a(A131205(1+n)) = n.

%o (Scheme)

%o (define (A278163 n) (let loop ((k 0)) (if (>= (A131205 (+ 1 k)) n) k (loop (+ 1 k)))))

%o (definec (A131205 n) (if (= 1 n) 1 (+ (A000123 (- n 1)) (A131205 (- n 1)))))

%o ;; For other code, see A277903.

%Y Cf. A000123, A131205, A277903, A278164.

%K nonn

%O 1,4

%A _Antti Karttunen_, Nov 15 2016