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