A099332 Primes p such that p = a^2 + b^2 for a,b>0 and a+b is prime.

2, 5, 13, 17, 29, 37, 61, 73, 89, 97, 101, 109, 149, 157, 181, 193, 229, 241, 257, 269, 277, 293, 349, 409, 421, 433, 461, 521, 541, 593, 601, 641, 661, 701, 709, 733, 769, 797, 829, 853, 881, 929, 937, 953, 997, 1009, 1021, 1049, 1061, 1069, 1109, 1117

Offset

1,1

Comments

Let q=a+b. For a specific prime q, the number of distinct primes p that are the sum of two squares is A082519(q)/2.

Primes p of the form (q-b)^2 + b^2, where q is prime and 0<b<q.

Links

T. D. Noe, Table of n, a(n) for n=1..1000

Formula

Primes p such that p = (q^2 + x^2)/2, where q is prime and |x| < q. - Thomas Ordowski, Feb 15 2013

Example

29 is in this sequence because 29=2^2+5^2 and 2+5 is prime.

Mathematica

Needs["NumberTheory`NumberTheoryFunctions`"]; lst={2}; Do[n=4k+1; If[PrimeQ[n], If[PrimeQ[Plus@@QuadraticRepresentation[1, n]], AppendTo[lst, n]]], {k, 500}]; lst

Crossrefs

Cf. A082519 (number of times that k^2 + (n-k)^2 is prime for 1 <= k <= n-1).

Sequence in context: A177349 A160215 A068486 * A279687 A031439 A074856

Adjacent sequences: A099329 A099330 A099331 * A099333 A099334 A099335

Keyword

nonn

Author

T. D. Noe, Oct 15 2004

Status

approved