A263980 Least prime of the form a^2 + b^2 with a > k and b > k, for some number k.

2, 13, 41, 61, 113, 181, 269, 313, 421, 613, 761, 929, 1013, 1201, 1301, 1637, 1741, 1861, 2113, 2381, 2521, 2969, 3121, 3449, 3613, 4153, 4337, 4513, 5101, 5737, 5953, 6173, 6389, 6857, 7321, 7817, 8069, 8581, 9397, 9661, 9941, 10513, 11717, 12329, 12641, 13613, 14281, 14621, 15313, 16381, 17117, 17489, 18253, 18637, 19013, 19801, 20201

Offset

1,1

Comments

List of distinct members of A263979.

The sequence is infinite; see Sierpinski (1988), p. 221.

References

W. Sierpinski, Elementary Theory of Numbers, 2nd English edition, revised and enlarged by A. Schinzel, Elsevier, 1988.

Links

Table of n, a(n) for n=1..57.

Formula

a(n) == 1 or 2 mod 4.

Example

The smallest prime of the form a^2 + b^2 with a > 2 and b > 2 is 41 = 4^2 + 5^2, so 41 is a member.
5 = 1^2 + 2^2 is a prime of the form a^2 + b^2 with a > 0 and b > 0, but 5 is not a member, because 2 = 1^2 + 1^2 is a smaller prime of that form.

Mathematica

Union[Table[
  Min[Select[
    Union[
     Flatten[
      With[{n = k},
       Array[#1^2 + #2^2 &, { 2 n + 1, 2 n + 1}, {n + 1, n + 1}]]]],
    PrimeQ]], {k, 0, 99}]]

Crossrefs

Cf. A002144, A002313, A263979.

Sequence in context: A042795 A361071 A179925 * A157185 A219054 A154354

Adjacent sequences: A263977 A263978 A263979 * A263981 A263982 A263983

Keyword

nonn

Author

Jonathan Sondow, Nov 09 2015

Status

approved