Arithmetic progressions of primes and sums of squares

[Don Reble]

Seqfans, Dr. Guy:

> I wrote a Fortran program...
	You poor fellow. :-(

> My a(7) seems to be correct, with the progression
> 7,157,307,457,607,757,907.
    Yes.
    That 1307 is an easy mistake to make. If one mistakenly believes
    that the gap must be >= 2*3*5*7, he won't find your progression.

    Dr Guy's UPiNT2 A5 is interesting. He has A005115 there, with
    l(7)=1307, even though the next paragraph refutes it:
    "(q,d)=(7,150)". Alas, he has just sent UPiNT3 to the publisher;
    no doubt he will fix UPiNT4.

> Currently I'm searching for a(15)...
    If I may steal your thunder,
    a(15)=173471351, gap(15)=4144140
    a(16)=198793279, gap(16)=9699690 (This one's in UPiNT2 A5.)

    Dr Guy doesn't claim that the progressions of A5 have the lowest
    possible ending, so the other ones are only upper-bounds of A005115.
--
Don Reble       djr at nk.ca