A198799 - OEIS

%I #40 Dec 19 2022 10:17:33

%S 2,0,49,637,1729,8281,12103,1529437,53599,157339,593047,19882681,

%T 375193,68574961,2989441,7709611,1983163,47738317081,4877509,

%U 21169376772835837,18384457,377770939,69771386503,146482609,13882141,1302924259,3418797938647,92672671

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

%C 10^12 < a(19) <= 21169376772835837. a(20) = 18384457. a(21) = 377770939. - _Donovan Johnson_, Nov 07 2011

%H Seth A. Troisi, <a href="/A198799/b198799.txt">Table of n, a(n) for n = 0..1000</a>

%H Seth A. Troisi, <a href="https://github.com/sethtroisi/OEIS/tree/main/A198799">Python program</a>

%F A088534(a(n)) = n and A088534(m) <> n for m < a(n).

%e a(0) = A034020(1) = 2;

%e a(1) = A198772(1) = 0;

%e a(2) = A198773(1) = A118886(1) = 49;

%e a(3) = A198774(1) = A118886(28) = 637;

%e a(4) = A198775(1) = A118886(97) = 1729;

%e 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 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 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 (Haskell)

%o import Data.List (elemIndex)

%o import Data.Maybe (fromJust)

%o a198799 n = fromJust $ elemIndex n a088534_list

%o (PARI) a(n)=for(k=0,oo,A088534(k)==n&&return(k)) \\ _M. F. Hasler_, Mar 06 2018

%Y Cf. A300419 (analog, with x,y >= 1).

%K nonn

%O 0,1

%A _Reinhard Zumkeller_, Oct 30 2011

%E a(7)-a(18) from _Donovan Johnson_, Nov 07 2011

%E More terms from _Seth A. Troisi_, Apr 23 2022