[seqfan] Re: New(?) sequence

[israel at math.ubc.ca]

On Jan 22 2023, zak seidov via SeqFan wrote:

> {7,11,13,17,19,23} + n are primes for n = 
> {0,90,16050,19410,43770,1091250,1615830,1954350,2822700,2839920} 
and it continues 3243330, 3400200, 6005880, 6503580, 7187760, 7641360, 
8061990, 8741130, 10526550, 11086830, 11664540, 14520540, 14812860, 
14834700, 14856750, 16025820, 16094700, 18916470, 19197240, 19634040, 
19800360, 20112210, 20247030, 21321180, 21850170, 22587270, 24786390, 
25009410, 25524120, 27305550, 29153550, 31563930, 31875570, 32836740, 
33575940, 36319170, 36985290, 37055640, 40660710, 41214060, 41763420, 
41927430, 44842860, 45974550, 47204730, 48660240, 49157730, 50685900, 
50943780, 51255630, 53204850, 53266380, 55057890, 56431920, 57812460, 
59877390, 61052340, 62757960, 63655710, 65689560, 67022220, 69296310, 
72610110, 74283600, 74390070, 75085590, 76150500, 79413060, 82984530, 
87423090, 89483820, 94752720, ...

More generally, you can have a similar sequence for primes 
{p(j), p(j+1), ..., p(k)} as long as these don't cover all residues mod
any of p(j) to p(k).

>29 + n's are not primes :(

In case you missed it, that's because {7,11,13,17,19,23,29} cover all 
residues mod 7, so at least one of {7,11,13,17,19,23,29} + n will be 
divisible by 7.

Cheers,
Robert

>Zak Seidov
>zakseidov at yahoo.com
>
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