A127079 Number of ways to represent prime(n) as a+b with a >= b > 0 and a^2+b^2 prime.

1, 1, 2, 2, 3, 3, 4, 4, 4, 6, 5, 8, 9, 7, 7, 9, 9, 11, 11, 9, 11, 13, 15, 14, 14, 18, 16, 17, 16, 20, 18, 22, 18, 21, 23, 21, 24, 24, 22, 24, 22, 28, 30, 23, 27, 24, 29, 30, 30, 28, 29, 24, 28, 30, 34, 33, 36, 35, 31, 37, 32, 36, 37, 41, 42, 42, 42, 43, 42, 38, 34, 43, 38, 45, 44

Offset

1,3

Comments

Essentially A036468 restricted to the primes.

a(n) <= floor(prime(n)/2).

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Example

prime(5) = 11 can be represented as 10+1, 9+2, 8+3, 7+4 and 6+5. Among 10^2+1^2 = 101, 9^2+2^2 = 85, 8^2+3^2 = 73, 7^2+4^2 = 65 and 6^2+5^2 = 61 are three primes, hence a(5) = 3.

Maple

f:= proc(n) local a;
add(charfcn[{true}](isprime(a^2 + (n-a)^2)), a=1..n/2)
end proc:
map(f, [seq(ithprime(i), i=1..100)]); # Robert Israel, Jun 03 2019

Mathematica

Reap[Do[p = Prime[n]; c = 0; Do[b = p - a; If[PrimeQ[a^2 + b^2], c++], {a, 1, p/2}]; Sow[c], {n, 1, 75}]][[2, 1]] (* Jean-François Alcover, Aug 19 2020 *)

Prog

(PARI) {for(n=1, 75, p=prime(n); c=0; for(a=1, p\2, b=p-a; if(isprime(a^2+b^2), c++)); print1(c, ", "))} /* Klaus Brockhaus, Mar 26 2007 */

Crossrefs

Cf. A036468.

Sequence in context: A076890 A103358 A063084 * A080251 A220032 A219773

Adjacent sequences: A127076 A127077 A127078 * A127080 A127081 A127082

Keyword

nonn

Author

J. M. Bergot, Mar 24 2007

Extensions

Edited and extended by Klaus Brockhaus, Mar 26 2007

Status

approved