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A226539 Numbers which are the sum of two squared primes in exactly two ways (ignoring order). 3
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 (list; graph; refs; listen; history; text; internal format)
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 *)

CROSSREFS

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

Cf. A045636 (sum of two prime squares is 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

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Last modified June 28 19:36 EDT 2017. Contains 288840 sequences.