# Number of positive solutions of the Diophantine x*p+y*q=(p+q)^3,

Jacques Tramu jacques.tramu at echolalie.com
Tue Feb 26 14:25:38 CET 2008

Correct ?
Yes, checked with another program and found same sequence, up to n=100.
Other terms : (n,number of solutions) :

10      241
100     4353
1000    63385
10000   837889
100000  10397721
1000000 123886921
10000000        1435397457
100000000       16304597977
1000000000      182414108009
10000000000     2016782405009

Regards,
Jacques.

---------------------------------------------------------
----- Original Message -----
From: "zak seidov" <zakseidov at yahoo.com>

> Dear seqfans,
> is it
> new/correct/interesting/nice,
> or
> old/wrong/dumb?
> thanks, zak
>
> 21,34,49,76,97,122,145,169,211,241,274,313,337,361,401,449,481,513,553,577,609,649,689,745,793,817,841,865,889,963,1033,1073,1105,1153,1201,1233,1281,1321,1361,1409,1441,1489,1537,1561,1585,1641,1737,1801,1825,1849,1889,1921,1969,2033,2081,2129,2161,2193,2233,2257,2305,2401,2473,2497,2521,2593,2673,2737,2785,2809,2849,2905,2961,3009,3049,3089,3145,3193,3241,3313,3361,3409,3457,3489,3529,3569,3625,3673,3697,3721,3785,3865,3913,3961,4009,4049,4121,4177,4257,4353
> %N A000001 Number of positive solutions of the
> Diophantine x*p+y*q=(p+q)^3, p=n-th prime, q=(n+1)-th
> prime.

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