[seqfan] Re: Question from Harvey Dale about A233552

[David Radcliffe]

All of the terms listed in A233552 are correct, but many are missing. Here
are the correct initial terms for A233552:
25, 49, 121, 169, 289, 361, 529, 625, 841, 919, 961, 1225, 1369, 1681,
1849, 2209, 2401, 2419, 2629, 2809, 3025

All numbers of the form (6k + 1)^2 or (6k - 1)^2 with k >= 1 are terms.

The following numbers are terms because they have covering sets of prime
divisors:
919, 2419, 2629, 3301, 5209, 5539, 5581, 6421, 7771, 8551, 9109, 9871,
10039, 10819, 11491, 13399, 13729, 13771, 14611, 15661, 15961, 16741,
17299, 18061, 18229, 18799, 19009, 19681, 21589, 21919, 21961, 24151,
24931, 25489

The covering set for 15661 is {3,5,7,17,241}. For the rest, {3,5,7,11,13}
is a covering set, not necessarily minimal.

The following numbers have unknown status. For each n in this list, I have
not found k < 10000 such that (n*4^k-1)/3 is a pseudoprime, nor have I
found a covering set.

3145, 3991, 5461, 6019, 7309, 8869, 12091, 14701, 18439, 19651, 20569,
21289, 21781, 22171, 22285, 22519, 22789, 22891