A226599 Numbers which are the sum of two squared primes in exactly four ways (ignoring order).

10370, 10730, 11570, 12410, 13130, 19610, 22490, 25010, 31610, 38090, 38930, 39338, 39962, 40970, 41810, 55250, 55970, 59330, 59930, 69530, 70850, 73730, 76850, 77090, 89570, 98090, 98930, 103298, 118898, 125450, 126290, 130730, 135218, 139490

Offset

1,1

Comments

It appears that all first differences are divisible by 24. - Zak Seidov, Jun 14 2013

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

Formula

a(n) = p^2 + q^2; p, q are (not necessarily different) primes

Example

10370 = 13^2 + 101^2 = 31^2 + 97^2 = 59^2 + 83^2 = 71^2 + 73^2.
10730 = 11^2 + 103^2 = 23^2 + 101^2 = 53^2 + 89^2 = 67^2 + 79^2.

Maple

Prime2PairsSum := s -> select(x ->`if`(andmap(isprime, x), true, false),
   numtheory:-sum2sqr(s)):
for n from 2 to 10^6 do
  if nops(Prime2PairsSum(n)) = 4 then print(n, Prime2PairsSum(n)) fi;
od;

Mathematica

(* Assuming mod(a(n), 24) = 2 *) Reap[ For[ k = 2, k <= 2 + 240000, k = k + 24, pr = Select[ PowersRepresentations[k, 2, 2], PrimeQ[#[[1]]] && PrimeQ[#[[2]]] &]; If[Length[pr] == 4 , Print[k]; Sow[k]]]][[2, 1]] (* Jean-François Alcover, Jun 14 2013 *)

Crossrefs

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

Cf. A045636 (sum of two squared primes is a superset).

Cf. A214511 (least number having n representations).

Cf. A225104 (numbers having at least three representations is a superset).

Cf. A226539, A226562 (sums decomposed in exactly two and three ways).

Sequence in context: A234907 A180460 A035912 * A305332 A271766 A104439

Adjacent sequences: A226596 A226597 A226598 * A226600 A226601 A226602

Keyword

nonn

Author

Henk Koppelaar, Jun 13 2013

Status

approved