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

1,1

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

Example

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

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 *)

Prog

(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

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).

Sequence in context: A084231 A243483 A234625 * A066478 A261707 A202443

Adjacent sequences: A226536 A226537 A226538 * A226540 A226541 A226542

Keyword

nonn

Author

Henk Koppelaar, Jun 10 2013

Extensions

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

Status

approved