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a(0)=1, after which a(n) = Number of terms of A005228 which occur between each consecutive terms of A232739, in range A232739(n)..A232739(n+1).
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%I #21 Jun 03 2018 03:47:05

%S 1,1,0,1,1,0,1,1,0,1,1,1,0,1,1,1,0,1,1,1,0,1,1,1,1,0,1,1,1,1,0,1,1,1,

%T 1,1,0,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,0,1,1,1,1,1,1,0,1,1,1,1,1,1,

%U 0,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,1,1,1,1,1,1,1,1,0,1

%N a(0)=1, after which a(n) = Number of terms of A005228 which occur between each consecutive terms of A232739, in range A232739(n)..A232739(n+1).

%C Does a term larger than 1 ever appear?

%C Positions of zeros: 2, 5, 8, 12, 16, 20, 25, 30, 36, 42, 48, 54, 61, 68, 76, 84, 92, 101, 110, 119, 128, ...

%C and their first differences: 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 6, 7, 7, 8, 8, 8, 9, 9, 9, 9, 10, 10, 11, 11, 11, 12, 11, 13, 12, 13, ...

%C might be also interesting.

%H Antti Karttunen, <a href="/A232750/b232750.txt">Table of n, a(n) for n = 0..2096</a>

%H <a href="/index/Ho#Hofstadter">Index entries for Hofstadter-type sequences</a>

%F a(n) = A232746(A232739(n+1)) - A232746(A232739(n)).

%e The two sequences begin as:

%e A232739: 2, 4,6, 9, 13,17, 22, 28,34, 41, 49, 58,67, 77, ...

%e A005228: 1, 3, 7, 12, 18, 26, 35, 45, 56, 69, 83, ...

%e We let a(0)=1 stand for the number of terms of A005228 that are before the first term of A232739, namely that 1 which is less than 2, and thereafter we count the terms of A005228 that occur between each two consecutive terms of A232739, noting that 3 in the latter occurs between 2 and 4 in the former, thus a(1)=1, no terms in the latter occur between 4 and 6 in the former, thus a(2)=0, 7 in the latter occurs between 6 and 9 in the former, thus a(3)=1, and so on. See also the example in A232740.

%o (Scheme)

%o (define (A232750 n) (if (zero? n) 1 (- (A232746 (A232739 (+ n 1))) (A232746 (A232739 n)))))

%Y Cf. A005228, A232739, A232740, A232746.

%K nonn

%O 0

%A _Antti Karttunen_, Dec 04 2013