A226599 - OEIS

%I #17 Sep 20 2018 00:30:43

%S 10370,10730,11570,12410,13130,19610,22490,25010,31610,38090,38930,

%T 39338,39962,40970,41810,55250,55970,59330,59930,69530,70850,73730,

%U 76850,77090,89570,98090,98930,103298,118898,125450,126290,130730,135218,139490

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

%C It appears that all first differences are divisible by 24. - _Zak Seidov_, Jun 14 2013

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

%H T. D. Noe, <a href="/A226599/b226599.txt">Table of n, a(n) for n = 1..10000</a>

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

%e 10370 = 13^2 + 101^2 = 31^2 + 97^2 = 59^2 + 83^2 = 71^2 + 73^2.

%e 10730 = 11^2 + 103^2 = 23^2 + 101^2 = 53^2 + 89^2 = 67^2 + 79^2.

%p Prime2PairsSum := s -> select(x ->`if`(andmap(isprime, x), true, false),

%p    numtheory:-sum2sqr(s)):

%p for n from 2 to 10^6 do

%p   if nops(Prime2PairsSum(n)) = 4 then print(n, Prime2PairsSum(n)) fi;

%p od;

%t (* 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 *)

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

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

%Y Cf. A214511 (least number having n representations).

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

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

%K nonn

%O 1,1

%A _Henk Koppelaar_, Jun 13 2013