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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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

A145376 If T(n)>=n is the nearest triangular number to n and p_n is the n-th prime, then a(n) is the least prime such that T(a(n)*p_n)-a(n)p_n is a triangular number.

Original entry on oeis.org

3, 2, 2, 2, 2, 3, 5, 5, 7, 11, 11, 11, 13, 17, 17, 19, 23, 23, 23, 29, 29, 29, 31, 37, 37, 41, 41, 41, 41, 43, 53, 53, 53, 59, 59, 61, 67, 67, 67, 71, 73, 73, 79, 79, 83, 83, 89, 97, 97, 97, 97, 101, 101, 107, 107, 113, 113, 127, 127, 127, 127, 127, 131, 137
Offset: 1

Views

Author

Vladimir Shevelev, Oct 09 2008

Keywords

Comments

Conjecture. For n>=2 the sequence is nondecreasing.
The conjecture holds for the first 10000 terms. [Charles R Greathouse IV, Feb 21 2011]

Links

Crossrefs

Cf. A000217, A145043, A145016, A145281, A145300.

Extensions

a(27)-a(64) from Charles R Greathouse IV, Feb 21 2011
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