A232750 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).

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, 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, 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

Offset

0

Comments

Does a term larger than 1 ever appear?

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

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, ...

might be also interesting.

Links

Antti Karttunen, Table of n, a(n) for n = 0..2096

Index entries for Hofstadter-type sequences

Formula

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

Example

The two sequences begin as:
A232739:  2,  4,6,  9,  13,17,   22,   28,34,  41,  49,   58,67,   77,   ...
A005228: 1, 3,    7, 12,      18,   26,     35,  45,   56,      69,   83, ...
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.

Prog

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

Crossrefs

Cf. A005228, A232739, A232740, A232746.

Sequence in context: A014768 A015527 A276395 * A080764 A291137 A285421

Adjacent sequences: A232747 A232748 A232749 * A232751 A232752 A232753

Keyword

nonn

Author

Antti Karttunen, Dec 04 2013

Status

approved