cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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A145047 Primes p of the form 4k+1 for which s=10 is the least positive integer such that sp-(floor(sqrt(sp)))^2 is a square.

Original entry on oeis.org

1237, 1621, 1721, 1933, 1949, 1993, 2221, 2237, 2309, 2341, 2473, 2621, 2657, 2789, 2797, 2857, 2953, 3221, 3361, 3533, 3677, 3881, 3889, 3917, 4133, 4457, 4481, 4549, 4813, 4889, 4973, 5153, 5189, 5261, 5441, 5653, 5717, 5813, 6101, 6217, 6301, 6329
Offset: 1

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Author

Vladimir Shevelev, Sep 30 2008, Oct 05 2008

Keywords

Comments

Conjecture: The least positive integer s can take values only from A008784 (see for s=1,2,5,10 sequences A145016, A145022, A145023 and this sequence).

Examples

			a(1)=1237 since p=1237 is the least prime of the form 4k+1 for which sp-(floor(sqrt(sp)))^2 is not a square for s=1..9, but 10p-(floor(sqrt(10p)))^2 is a square (for p=1237 it is 49).

Crossrefs

Cf. A145016, A145017, A145022, A145023, A008784.

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.

Original entry on oeis.org

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

Views

Author

Vladimir Shevelev, Sep 30 2008, Oct 03 2008

Keywords

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).

Examples

			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.

Extensions

More terms from Jinyuan Wang, Jul 16 2025
Showing 1-2 of 2 results.

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