# [seqfan] An idea of new 4 sequences

Sat Oct 19 10:25:25 CEST 2013

```Dear SeqFans,

I propose an idea of the following interesting new sequences (below
odious and evil numbers are in A000069 and A001969 respectively):

1) a(n) is the smallest odious number which can be written as a product of n, but not less than n, evil numbers, n>=2;
2) b(n)  is the smallest odious number which can be written as a product of n, but not less than n, odious numbers>1, n>=1;
3) c(n)  is the smallest evil number which can be written as a product of n, but not less than n, evil numbers, n>=1;
4)  d(n)  is the smallest evil number which can be written as a product of n, but not less than n, odious numbers>1, n>=2.

For example, a(2)=25, a(3)=575, a(4)=51175, a(5)=4554575. The two latter terms were calculated by Peter Moses.
E.g., the calculation a(4) is connected with the finding 4 evil primes p,q,r,s with the smallest their product, such that all 11 numbers p*q,p*r, p*s, q*r,q*s, r*s, p*q*r,p*q*s,p*r*s,q*r*s,p*q*r*s* are odious. Peter found p=5, q=5, r=23, s=89.
It is essentially a multiplicative variant of my previous "additive" problem (see my message and Maximilian's numerical results).

Best regards,