A226562 Numbers which are the sum of two squared primes in exactly three ways (ignoring order).

2210, 3770, 5330, 6290, 12818, 16490, 18122, 19370, 24050, 24650, 26690, 32810, 33410, 34970, 36530, 39650, 39770, 44642, 45050, 45890, 49010, 50690, 51578, 57770, 59450, 61610, 63050, 66170, 67490, 72410, 73610, 74210, 80330, 85202, 86210, 86330, 88010

Offset: 1

Author

Henk Koppelaar, Jun 11 2013

Keywords

• nonn

Comments

Suggestion: difference between successive terms is always at least 3. (With the known 115885 terms <10^9, the smallest difference is 24.) - Zak Seidov, Jun 12 2013

Examples

			2210 = 19^2 + 43^2 = 23^2 + 41^2 = 29^2 + 37^2;
		

References

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

Links

• Zak Seidov, Table of n, a(n) for n = 1..2464 (all terms up to 10^7).

Crossrefs

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

Cf. A045636 (sum of two squared primes), A226539.

Cf. A214511 (least number having n representations).

Cf. A226539 (restricted to sums decomposed in exactly three ways).

Programs

Maple

Prime2PairsSum := s -> select( x -> `if`(andmap(isprime, x), true, false), numtheory:-sum2sqr(s)):
for n from 2 to 10 do
if nops(Prime2PairsSum(n)) = 3 then print(n,Prime2PairsSum(n)) fi
od;

Mathematica

Select[Range@20000, Length[Select[ PowersRepresentations[#, 2, 2], And @@ PrimeQ[#] &]] == 3 &] (* Giovanni Resta, Jun 11 2013 *)

Extensions

a(22)-a(37) from Giovanni Resta, Jun 11 2013