A273859 The successive numbers of integers visible between two primes are given by the sequence itself.

0, 1, 2, 3, 4, 5, 6, 8, 7, 9, 10, 12, 11, 14, 15, 16, 18, 13, 20, 21, 22, 24, 25, 17, 26, 27, 28, 30, 32, 33, 19, 34, 35, 36, 38, 39, 40, 42, 44, 23, 45, 46, 48, 49, 50, 51, 52, 29, 54, 55, 56, 57, 58, 60, 62, 63, 64

Offset

1,3

Comments

The sequence starts with a(1)=0. It is then extended with the smallest integer not yet present and not leading to a contradiction. This sequence is a permutation of the integers >=0

Links

Table of n, a(n) for n=1..57.

Example

The first two primes that appear in the sequence are 2 and 3; between 2 and 3 there are 0 integers and this 0 corresponds to the starting 0 of the sequence.
The next prime is 5 and between 3 and 5 there is 1 integer [which is 4] and this 1 corresponds to the next term of the sequence.
The next prime is 7 and between 5 and 7 there are 2 integers [which are 6 and 8] and this 2 corresponds to the next term of the sequence.
The next prime is 11 and between 7 and 11 there are 3 integers [which are 9, 10 and 12] and this 3 corresponds to the next term of the sequence.
The next prime is 13 and between 11 and 13 there are 4 integers [which are 14, 15, 16 and 18] and this 4 corresponds to the next term of the sequence.
Etc.

Crossrefs

Sequence in context: A122349 A127388 A307032 * A332073 A117332 A368578

Adjacent sequences: A273856 A273857 A273858 * A273860 A273861 A273862

Keyword

nonn,base

Author

Eric Angelini, Jun 01 2016

Status

approved