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

2, 0, 49, 637, 1729, 8281, 12103, 1529437, 53599, 157339, 593047, 19882681, 375193, 68574961, 2989441, 7709611, 1983163, 47738317081, 4877509, 21169376772835837, 18384457, 377770939, 69771386503, 146482609, 13882141, 1302924259, 3418797938647, 92672671

Offset

0,1

Comments

10^12 < a(19) <= 21169376772835837. a(20) = 18384457. a(21) = 377770939. - Donovan Johnson, Nov 07 2011

Links

Seth A. Troisi, Table of n, a(n) for n = 0..1000

Seth A. Troisi, Python program

Formula

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

Example

a(0) = A034020(1) = 2;
a(1) = A198772(1) = 0;
a(2) = A198773(1) = A118886(1) = 49;
a(3) = A198774(1) = A118886(28) = 637;
a(4) = A198775(1) = A118886(97) = 1729;
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;
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.
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

Prog

(Haskell)
import Data.List (elemIndex)
import Data.Maybe (fromJust)
a198799 n = fromJust $ elemIndex n a088534_list
(PARI) a(n)=for(k=0, oo, A088534(k)==n&&return(k)) \\ M. F. Hasler, Mar 06 2018

Crossrefs

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

Sequence in context: A097173 A009493 A009718 * A156501 A012420 A140800

Adjacent sequences: A198796 A198797 A198798 * A198800 A198801 A198802

Keyword

nonn

Author

Reinhard Zumkeller, Oct 30 2011

Extensions

a(7)-a(18) from Donovan Johnson, Nov 07 2011

More terms from Seth A. Troisi, Apr 23 2022

Status

approved