A242991 Smallest prime p such that p - floor(sqrt(p))^2 = n^2.

2, 13, 73, 97, 281, 397, 1493, 1153, 2017, 2909, 4217, 6073, 8269, 12517, 13681, 17417, 22193, 26893, 34217, 40801, 51517, 60509, 72353, 89977, 101749, 115597, 151273, 158393, 180617, 204301, 237157, 278753, 335173, 336397, 388109, 435577, 477469, 527069, 585217, 652849, 717397

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

Cf. A145016.

Sequence in context: A289790 A109112 A163190 * A240549 A004027 A263840

Adjacent sequences: A242988 A242989 A242990 * A242992 A242993 A242994

Keyword

nonn

Author

Thomas Ordowski, Aug 17 2014

Extensions

More terms from Derek Orr, Aug 17 2014

Status

approved