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URL: https://oeis.org/A263980

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A263980
Least prime of the form a^2 + b^2 with a > k and b > k, for some number k.
1
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.
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
KEYWORD
nonn
AUTHOR
Jonathan Sondow, Nov 09 2015
STATUS
approved