A373947 Halved and run-compressed first differences of consecutive odd primes.

1, 2, 1, 2, 1, 2, 3, 1, 3, 2, 1, 2, 3, 1, 3, 2, 1, 3, 2, 3, 4, 2, 1, 2, 1, 2, 7, 2, 3, 1, 5, 1, 3, 2, 3, 1, 5, 1, 2, 1, 6, 2, 1, 2, 3, 1, 5, 3, 1, 3, 2, 1, 5, 7, 2, 1, 2, 7, 3, 5, 1, 2, 3, 4, 3, 2, 3, 4, 2, 4, 5, 1, 5, 1, 3, 2, 3, 4, 2, 1, 2, 6, 4, 2, 4, 2, 3

Offset

1,2

Comments

We define the run-compression of a sequence to be the anti-run obtained by reducing each run of repeated parts to a single part. Alternatively, run-compression removes all parts equal to the part immediately to their left. For example, (1,1,2,2,1) has run-compression (1,2,1).

Links

Table of n, a(n) for n=1..87.

Formula

a(n) = A037201(n+1)/2.

Example

The odd primes begin:
3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, ...
with differences:
2, 2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, ...
with run-compression:
2, 4, 2, 4, 2, 4, 6, 2, 6, 4, 2, 4, 6, 2, 6, 4, 2, 6, 4, 6, 8, 4, 2, 4, ...
which is 2*a(n).

Mathematica

First/@Split[Differences[Select[Range[3, 100], PrimeQ]]]/2

Crossrefs

Half of A037201(n+1).

Run-compression of A001223.

A003242, A114901, A116608, A116861, A238279, A240085, A333755, A373948, A373949, A373951, A373953, A373954.

Sequence in context: A361477 A331366 A274225 * A028334 A083269 A097306

Adjacent sequences: A373944 A373945 A373946 * A373948 A373949 A373950

Keyword

nonn

Author

Gus Wiseman, Jun 29 2024

Status

approved