A327797
Values of y in the n solutions corresponding to the least number A300419(n) expressible in exactly n ways as x^2 + x*y + y^2 with x >= y >= 1, with y written as triangle T(n,k), k <= n. x is given in A327796.
Original entry on oeis.org
1, 5, 1, 12, 7, 4, 23, 15, 8, 3, 91, 74, 61, 26, 7, 61, 49, 34, 27, 21, 2, 343, 273, 208, 200, 145, 133, 77, 122, 102, 90, 85, 58, 43, 25, 3, 225, 202, 182, 137, 117, 103, 70, 35, 13, 427, 389, 343, 317, 238, 189, 147, 107, 97, 14
Offset: 1
The triangle begins
1,
5, 1,
12, 7, 4,
23, 15, 8, 3,
91, 74, 61, 26, 7,
61, 49, 34, 27, 21, 2,
343, 273, 208, 200, 145, 133, 77,
122, 102, 90, 85, 58, 43, 25, 3
A300419
Smallest nonnegative number k such that k can be written in exactly n ways as x^2 + xy + y^2 where x and y are positive integers, with x >= y.
Original entry on oeis.org
0, 3, 91, 637, 1729, 24843, 12103, 405769, 53599, 157339, 593047, 59648043, 375193, 2989441, 8968323, 7709611, 1983163, 3360173089, 4877509, 2339177536969, 18384457, 377770939, 146482609, 439447827, 13882141, 1302924259
Offset: 0
a(2) = 91 because 91 = 1^2 + 1*9 + 9^2 = 5^2 + 5*6 + 6^2 and 91 is the least number with this property.
-
nmx = 4750; t = Split@ Sort@ Flatten@ Table[x^2 + x*y + y^2, {x, nmx}, {y, x, nmx}]; lmt = 1 + Length@ t; f[n_] := Block[{k = 1}, While[Length@ t[[k]] != n && k < lmt, k++]; t[[k]][[1]]]; Array[f, 16] (* Robert G. Wilson v, Mar 06 2018 *)
-
N(n,d)=sum(x=1,sqrt(n\3),sum(y=max(x,sqrtint(n-x^2)\2),sqrtint(n-2*x^2),x^2+x*y+y^2==n&&!(d&&printf("%d",[x,y])))) \\ Set 2nd arg = 1 to display all decompositions.
a(n)=for(k=0,oo,N(k)==n&&return(k))
Showing 1-2 of 2 results.
Comments