A226539 Numbers which are the sum of two squared primes in exactly two ways (ignoring order).

338, 410, 578, 650, 890, 1010, 1130, 1490, 1730, 1802, 1898, 1970, 2330, 2378, 2738, 3050, 3170, 3530, 3650, 3842, 3890, 4010, 4658, 4850, 5018, 5090, 5162, 5402, 5450, 5570, 5618, 5690, 5858, 6170, 6410, 6530, 6698, 7010, 7178, 7202, 7250, 7850, 7970, 8090

Offset: 1

Author

Henk Koppelaar, Jun 10 2013

Keywords

• nonn

Examples

			338 = 7^2 + 17^2 = 13^2 + 13^2;
410 = 7^2 + 19^2 = 11^2 + 17^2.
		

References

• Stan Wagon, Mathematica in Action, Springer, 2000 (2nd ed.), Ch. 17.5, pp. 375-378.

Links

• T. D. Noe, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A054735 (restricted to twin primes), A037073, A069496.

Cf. A045636 (sum of two squared primes: a superset).

Cf. A214511 (least number having n representations).

Cf. A226562 (restricted to sums decomposed in exactly three ways).

Programs

Maple

Prime2PairsSum := p -> select(x ->`if`(andmap(isprime, x),true,false), numtheory:-sum2sqr(p)):
for n from 2 to 10^6 do
  if nops(Prime2PairsSum(n)) = 2 then print(n, Prime2PairsSum(n)) fi;
od;

Mathematica

Select[Range@10000, Length[Select[ PowersRepresentations[#, 2, 2], And @@ PrimeQ[#] &]] == 2 &] (* Giovanni Resta, Jun 11 2013 *)

PARI

select( is_A226539(n)={#[0|t<-sum2sqr(n),isprime(t[1])&&isprime(t[2])]==2}, [1..10^4]) \\ For more efficiency, apply selection to A045636. See A133388 for sum2sqr(). - M. F. Hasler, Dec 12 2019

Extensions

a(25)-a(44) from Giovanni Resta, Jun 11 2013