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

1,1

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

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).

Example

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

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 *)

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).

Sequence in context: A043659 A178458 A248712 * A300166 A031772 A305880

Adjacent sequences: A226559 A226560 A226561 * A226563 A226564 A226565

Keyword

nonn

Author

Henk Koppelaar, Jun 11 2013

Extensions

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

Status

approved