A232740 - OEIS

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A232740

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

1, 2, 1, 2, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

Do any other values appear than 1 and 2? The 2's seem to be getting rarer, as zeros correspondingly get rarer in A232750. This has some implications about how the ratio A005228(n)/A232739(n) will develop. Please see also the comments and graph-drawing link in A232739.

LINKS

Antti Karttunen, Table of n, a(n) for n = 1..2009

Index entries for Hofstadter-type sequences

FORMULA

a(n) = A232753(A005228(n+1)) - A232753(A005228(n)).

EXAMPLE

The two sequences begin as:

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

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

Grouping together the terms of A232739 that occur between two successive terms of A232739, we get {2}, {4,6}, {9}, {13,17}, {22}, {28,34}, {41}, {49}, {58,67}, {77}, ... and counting how many terms are in each such group, we get 1, 2, 1, 2, 1, 2, 1, 1, 2, 1, ..., the first terms of this sequence.

PROG

(Scheme)

(define (A232740 n) (- (A232753 (A005228 (+ n 1))) (A232753 (A005228 n))))

CROSSREFS

Cf. A005228, A232739, A232750, A232753.

Sequence in context: A210501 A307781 A356112 * A188512 A081129 A022934

Adjacent sequences: A232737 A232738 A232739 * A232741 A232742 A232743

KEYWORD

nonn

AUTHOR

Antti Karttunen, Dec 04 2013

STATUS

approved