cp's OEIS Frontend

A198799 Smallest m such that m can be written in exactly n ways as x^2 + xy + y^2 with 0 <= x <= y.

%I A198799 #40 Dec 19 2022 10:17:33
%S A198799 2,0,49,637,1729,8281,12103,1529437,53599,157339,593047,19882681,
%T A198799 375193,68574961,2989441,7709611,1983163,47738317081,4877509,
%U A198799 21169376772835837,18384457,377770939,69771386503,146482609,13882141,1302924259,3418797938647,92672671
%N A198799 Smallest m such that m can be written in exactly n ways as x^2 + xy + y^2 with 0 <= x <= y.
%C A198799 10^12 < a(19) <= 21169376772835837. a(20) = 18384457. a(21) = 377770939. - _Donovan Johnson_, Nov 07 2011
%H A198799 Seth A. Troisi, <a href="/A198799/b198799.txt">Table of n, a(n) for n = 0..1000</a>
%H A198799 Seth A. Troisi, <a href="https://github.com/sethtroisi/OEIS/tree/main/A198799">Python program</a>
%F A198799 A088534(a(n)) = n and A088534(m) <> n for m < a(n).
%e A198799 a(0) = A034020(1) = 2;
%e A198799 a(1) = A198772(1) = 0;
%e A198799 a(2) = A198773(1) = A118886(1) = 49;
%e A198799 a(3) = A198774(1) = A118886(28) = 637;
%e A198799 a(4) = A198775(1) = A118886(97) = 1729;
%e A198799 a(5) = 8281 = A118886(569) = 0 + 0*91 + 91^2 = 11^2 + 11*85 + 85^2 = 19^2 + 19*80 + 80^2 = 39^2 + 39*65 + 65^2 = 49^2 + 49*56 + 56^2;
%e A198799 a(6) = 12103 = A118886(862) = 2^2 + 2*109 + 109^2 = 21^2 + 21*98 + 98^2 = 27^2 + 27*94 + 94^2 = 34^2 + 34*89 + 89^2 = 49^2 + 49*77 + 77^2 = 61^2 + 61*66 + 66^2.
%e A198799 405769 = Q(0, 637) = Q(77, 595) = Q(133, 560) = Q(145, 552) = Q(200, 513) = Q(208, 507) = Q(273, 455) = Q(343, 392), where Q(x, y) = x^2 + xy + y^2 but it is not a(7) since sequence definition focuses 'exactly'. - _M. F. Hasler_, Mar 06 2018
%o A198799 (Haskell)
%o A198799 import Data.List (elemIndex)
%o A198799 import Data.Maybe (fromJust)
%o A198799 a198799 n = fromJust $ elemIndex n a088534_list
%o A198799 (PARI) a(n)=for(k=0,oo,A088534(k)==n&&return(k)) \\ _M. F. Hasler_, Mar 06 2018
%Y A198799 Cf. A300419 (analog, with x,y >= 1).
%K A198799 nonn
%O A198799 0,1
%A A198799 _Reinhard Zumkeller_, Oct 30 2011
%E A198799 a(7)-a(18) from _Donovan Johnson_, Nov 07 2011
%E A198799 More terms from _Seth A. Troisi_, Apr 23 2022