# [seqfan] Re: OEISWiki : decomposition into weight * level + jump

Rémi Eismann reismann at free.fr
Tue Jan 25 10:23:09 CET 2011

```Dear seqfans,

I finished submitting sequences related to the decomposition. There are 13 sequences decomposed on the OEIS:
If the decomposition is possible we have:
natural numbers: A000027(n) = A020639(n-1) * A032742(n-1) + 1 (l(n): A000027(n-1))
prime numbers: A000040(n) = A117078(n) * A117563(n) + A001223(n) (l(n): A118534(n))
odd numbers: A005408(n) = A090368(n-1) * A184726(n) + 2 (l(n): A005408(n-1))
even numbers: A005843(n) = A090369(n-1) * A184727(n) + 2 (l(n): A005843(n-1))
composite numbers: A002808(n) = A130882(n) * A179621(n) + A073783(n) (l(n): A179620(n))
semiprimes: A001358(n) = A130533(n) * A184729(n) + A065516(n) (l(n): A184728(n-1))
3-almost primes: A014612(n) = A130650(n) * A184753(n) + A114403(n) (l(n): A184752(n))
lucky numbers: A000959(n) = A130889(n) * A184828(n) + A031883(n) (l(n): A184827(n))
prime powers: A000961(n) = A184829(n) * A184831(n) + A057820(n) (l(n): A184830(n))
square free numbers: A005117(n) = A184832(n) * A184834(n) + A076259(n) (l(n): A184833(n))
triangular numbers: A000217(n) = A130703(n) * A184219(n) + (n + 1) (l(n): A184218(n))
squares: A000290(n) = A133150(n) * A184221(n) + A005408(n) (l(n): A184220(n))
pentagonal numbers: A000326(n) = A133151(n) * A184751(n) + A016777(n) (l(n): A184750(n))
All is on the OEIS Wiki page of the decomposition in weight * level + jump:
http://oeis.org/wiki/Decomposition_into_weight_*_level_%2B_jump
Have a nice day,

Rémi Eismann.

----- Mail Original -----
De: reismann at free.fr
À: seqfan at list.seqfan.eu
Envoyé: Mercredi 5 Janvier 2011 12:38:45 GMT +01:00 Amsterdam / Berlin / Berne / Rome / Stockholm / Vienne
Objet: OEISWiki : decomposition into weight * level + jump

Dear seqfans,

I edited the page "decomposition into weight * level + jump"
(and D. Forgues has improved the page, thank you to him).