A145050 Primes p of the form 4*k+1 for which s=26 is the least positive integer such that s*p-(floor(sqrt(s*p)))^2 is a square.

6569, 8117, 8689, 9221, 9281, 9829, 10289, 10457, 11597, 11953, 12577, 12721, 13093, 14561, 15737, 15817, 16529, 17041, 17341, 17737, 18089, 18397, 19121, 19997, 20129, 20693, 20789, 21601, 21701, 22093, 22433, 22777, 22877, 23029, 23633, 23833, 24809, 25589

Offset

1,1

Comments

For all primes of the form 4*k+1 not exceeding 10000 the least integer s takes only values: 1, 2, 5, 10, 13, 17, 26. These values are the first numbers in A145017 (see our conjecture at A145047).

Links

Table of n, a(n) for n=1..38.

Example

a(1)=6569 since p=6569 is the least prime of the form 4*k+1 for which s*p-(floor(sqrt(s*p)))^2 is not a square for s=1..25, but 26*p-(floor(sqrt(26*p)))^2 is a square (for p=6569 it is 225).

Crossrefs

Cf. A145016, A145017, A145022, A145023, A145043, A145047, A145048, A145049.

Sequence in context: A031579 A288884 A031759 * A319604 A256837 A216177

Adjacent sequences: A145047 A145048 A145049 * A145051 A145052 A145053

Keyword

nonn

Author

Vladimir Shevelev, Sep 30 2008, Oct 03 2008

Extensions

More terms from Jinyuan Wang, Jul 16 2025

Status

approved