A088919 - OEIS

%I #15 Jun 19 2013 06:19:06

%S 1,13,410,2210,10370,202130,229970,197210,81770,18423410,16046810,

%T 12625730,21899930,9549410,370247930,416392730,579994610,338609570,

%U 2155919090,601741010,254885930,10083683090,4690939370,29207671610

%N Smallest number having exactly n representations as sum of two squares of distinct primes.

%C A088918(a(n)) = n and A088918(k) <> n for k<a(n).

%C No terms after a(13) are smaller than 99000000. - _John W. Layman_, Jan 20 2004

%H Donovan Johnson, <a href="/A088919/b088919.txt">Table of n, a(n) for n = 0..33</a> (terms < 10^12)

%H <a href="/index/Su#ssq">Index entries for sequences related to sums of squares</a>

%e a(2) = 410 = 7^2+19^2 = 11^2+17^2;

%e a(3) = 2210 = 19^2+43^2 = 23^2+41^2 = 29^2+37^2;

%e a(4) = 10370 = 13^2+101^2 = 31^2+97^2 = 59^2+83^2 = 71^2+73^2;

%e a(5) = 202130 = 23^2+449^2 = 97^2+439^2 = 163^2+419^2 = 211^2+397^2 = 251^2+373^2;

%e a(6) = 229970 = 23^2+479^2 = 109^2+467^2 = 193^2+439^2 = 263^2+401^2 = 269^2+397^2 = 331^2+347^2;

%e a(7) = 197210 = 31^2+443^2 = 67^2+439^2 = 107^2+431^2 = 173^2+409^2 = 199^2+397^2 = 241^2+373^2 = 311^2+317^2;

%e a(8) = 81770 = 41^2+283^2 = 53^2+281^2 = 71^2+277^2 = 97^2+269^2 = 137^2+251^2 = 157^2+239^2 = 179^2+223^2 = 193^2+211^2.

%t (* This program is not convenient for a large number of terms *) nMax = 14; piMax = 2500; tp = Table[{Prime[i]^2 + Prime[j]^2, i, j}, {i, 1, piMax}, {j, i+1, piMax}] // Flatten[#, 1]&; sp = tp[[All, 1]] // Tally // Sort[#, #1[[2]] > #2[[2]]& ]& // Split[#, #1[[2]] == #2[[2]]& ]&; ssp = (Sort /@ sp)[[All, 1]]; a[0] = 1; Do[a[ssp[[n, 2]]] = ssp[[n, 1]], {n, 1, Length[ssp]}]; Table[a[n], {n, 0, nMax}] (* _Jean-François Alcover_, Jun 19 2013 *)

%K nonn

%O 0,2

%A _Reinhard Zumkeller_, Oct 23 2003

%E More terms from _John W. Layman_, Jan 20 2004

%E a(14)-a(23) from _Donovan Johnson_, May 08 2010