OFFSET
1,1
COMMENTS
Also the smallest prime p = n^2 + x^2 such that x > n^2/2.
For n < 10^6, a(7) > a(8) is the only place where the sequence is not increasing. - Derek Orr, Aug 17 2014
LINKS
Robert Israel, Table of n, a(n) for n = 1..9998
EXAMPLE
2 = 1^2 + 1^2,
13 = 2^2 + 3^2,
73 = 3^2 + 8^2,
97 = 4^2 + 9^2,
281 = 5^2 + 16^2,
397 = 6^2 + 19^2,
...
MAPLE
a:= proc(n) local x, p; for x from ceil(n^2/2) do p:= n^2+x^2; if isprime(p) then return(p) fi od end proc:
seq(a(n), n=1..100); # Robert Israel, Aug 17 2014
MATHEMATICA
spp[n_]:=Module[{p=2}, While[p-Floor[Sqrt[p]]^2!=n^2, p=NextPrime[p]]; p]; Array[spp, 50] (* Harvey P. Dale, Jan 10 2022 *)
PROG
(PARI)
a(n)=k=ceil(n^2/2); while(!ispseudoprime(n^2+k^2), k++); return(n^2+k^2)
vector(100, n, a(n)) \\ Derek Orr, Aug 17 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
Thomas Ordowski, Aug 17 2014
EXTENSIONS
More terms from Derek Orr, Aug 17 2014
STATUS
approved