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

0,2

Comments

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

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

Links

Donovan Johnson, Table of n, a(n) for n = 0..33 (terms < 10^12)

Index entries for sequences related to sums of squares

Example

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.

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 *)

Crossrefs

Sequence in context: A069876 A126086 A055203 * A201537 A258178 A266486

Adjacent sequences: A088916 A088917 A088918 * A088920 A088921 A088922

Keyword

nonn

Author

Reinhard Zumkeller, Oct 23 2003

Extensions

More terms from John W. Layman, Jan 20 2004

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

Status

approved