A143502 n occurs d(n-1) times.

2, 3, 3, 4, 4, 5, 5, 5, 6, 6, 7, 7, 7, 7, 8, 8, 9, 9, 9, 9, 10, 10, 10, 11, 11, 11, 11, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 15, 15, 15, 15, 16, 16, 16, 16, 17, 17, 17, 17, 17

Offset

1,1

Links

Table of n, a(n) for n=1..50.

Formula

A composite of infinite arithmetic sequences (1 mod k, k>1): (1, 2, 3,...), (1, 3, 5,...), (1, 4, 7,...)...; arranged in order of magnitude; and deleting the initial ones.

Example

Given an array of arithmetic sequences: k, (1 mod 2), ( 1 mod 3)...:
1,...2,...3,...4,...
1,...3,...5,...7,...
1,...4,...7,..10,...
1,...5,...9,..13,...
...
We extract all terms in the array (>1) and arrange in order of magnitude.
n occurs d(n-1) times where d(n) = A000005: (1, 2, 2, 3, 2, 4, 2, 4, 3, 4,...).
7 occurs 4 times in the following subsets, indicated by the divisors of (n-1): (n), (1 mod 2), (1 mod 3), (1 mod 6) = (1, 2, 3, 4, 5, 6, 7,...), (1, 3, 5, 7,...), (1, 4, 7, 10,...) and (1, 7, 13, 19,...).

Crossrefs

Cf. A000005.

Sequence in context: A060020 A300154 A166127 * A070984 A134995 A194243

Adjacent sequences: A143499 A143500 A143501 * A143503 A143504 A143505

Keyword

nonn

Author

Gary W. Adamson, Aug 21 2008

Status

approved