A088919 Smallest number having exactly n representations as sum of two squares of distinct primes.

1, 13, 410, 2210, 10370, 202130, 229970, 197210, 81770, 18423410, 16046810, 12625730, 21899930, 9549410, 370247930, 416392730, 579994610, 338609570, 2155919090, 601741010, 254885930, 10083683090, 4690939370, 29207671610

Offset: 0

Author

Reinhard Zumkeller, Oct 23 2003

Keywords

• nonn

Comments

A088918(a(n)) = n and A088918(k) <> n for k

No terms after a(13) are smaller than 99000000. - John W. Layman, Jan 20 2004

Examples

			a(2) = 410 = 7^2+19^2 = 11^2+17^2;
a(3) = 2210 = 19^2+43^2 = 23^2+41^2 = 29^2+37^2;
a(4) = 10370 = 13^2+101^2 = 31^2+97^2 = 59^2+83^2 = 71^2+73^2;
a(5) = 202130 = 23^2+449^2 = 97^2+439^2 = 163^2+419^2 = 211^2+397^2 = 251^2+373^2;
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;
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;
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.
		

Links

• Donovan Johnson, Table of n, a(n) for n = 0..33 (terms < 10^12)
• Index entries for sequences related to sums of squares

Programs

Mathematica

(* 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 *)

Extensions

More terms from John W. Layman, Jan 20 2004

a(14)-a(23) from Donovan Johnson, May 08 2010

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