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A357749 Sorted list of nonzero numbers x, y, z that occur in solutions to the equation (x + y)^2 + (y + z)^2 + (z + x)^2 = 12*x*y*z. 2
1, 3, 13, 61, 217, 291, 1393, 3673, 4683, 6673, 16693, 31971, 62221, 106153, 153181, 360517, 733933, 1054081, 1285131, 1709221, 2430493, 3516483, 4778353, 16848481, 17857153, 21717363, 27755113, 38745493, 55764867, 80725921, 98938381, 185236633, 302517517, 386781123 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..34.

Yasuaki Gyoda, Positive integer solutions to (x+y)^2+(y+z)^2+(z+x)^2=12xyz, arXiv:2109.09639 [math.NT], 2022.

EXAMPLE

The first few solutions are (x, y, z) = (1, 1, 1), (1, 1, 3), (1, 3, 13), (1, 13, 61), (1, 61, 291), (1, 291, 1393), (1, 1393, 6673), (1, 6673, 31971), (3, 13, 217), (3, 217, 3673), ..., so 1, 3, 13, 61, 217, 291, ... are terms.

PROG

(PARI) a357749(steps) = {L=List(); listput(L, [1, 1, 1]); listput(L, [1, 1, 3]); listput(L, [1, 13, 3]); for(n=1, steps, my(mp, mv); for(l=1, #L, mv=vecmax(L[l], &mp); my (a=L[l][1], b=L[l][2], c=L[l][3], s=a+b+c); if(mp==1, listput(L, [a, 6*a*c-s, c]); listput(L, [a, b, 6*a*b-s])); if(mp==2, listput(L, [6*b*c-s, b, c]); listput(L, [a, b, 6*a*b-s])); if(mp==3, listput(L, [6*b*c-s, b, c]); listput(L, [a, 6*a*c-s, c])))); M=List(); for (k=1, #L, for(j=1, 3, listput(M, L[k][j]))); vecsort(M, , 8)};

a357749(13)[1..35]

CROSSREFS

Cf. A002559, A101368, A357870.

Sequence in context: A355298 A328704 A341077 * A112568 A104089 A334150

Adjacent sequences: A357746 A357747 A357748 * A357750 A357751 A357752

KEYWORD

nonn

AUTHOR

Hugo Pfoertner, Oct 18 2022

STATUS

approved

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Last modified February 6 10:18 EST 2023. Contains 360104 sequences. (Running on oeis4.)