A344083 a(n) = f(x)+f(y)+f(z), where (x,y,h) is the n-th Pythagorean triple listed in (A046083, A046084, A009000), and f(m)=A176775(m) is the index of m as k-gonal number for the smallest possible k.

6, 9, 7, 11, 9, 9, 12, 10, 9, 10, 9, 11, 18, 10, 16, 9, 9, 20, 9, 7, 18, 9, 18, 15, 11, 14, 7, 12, 10, 13, 12, 7, 12, 15, 12, 17, 14, 18, 13, 9, 13, 14, 15, 10, 9, 7, 9, 21, 12, 10, 15, 23, 7, 9, 12, 20, 9, 18, 17, 28, 14, 16, 7, 21, 18, 24, 21, 21, 20, 16, 25

Offset

1,1

Comments

6 is the minimum possible value, and A176775(3,4,5) gives this minimum.

Conjecture: there are no other Pythagorean triples that give this minimum. In other words, it is the only triple with 3 A090467 terms.

Links

Michel Marcus, Table of n, a(n) for n = 1..12471 (hypotenuses <= 10000).

Prog

(PARI) tp(n) = my(k=3); while( !ispolygonal(n, k), k++); k; \\ A176774
itp(n) = my(m=tp(n)); (m-4+sqrtint((m-4)^2+8*(m-2)*n)) / (2*m-4); \\ A176775
f(v) = vecsum(apply(itp, v));
list(lim) = {my(v=List(), m2, s2, h2, h); for(middle=4, lim-1, m2=middle^2; for(small=1, middle, s2=small^2; if(issquare(h2=m2+s2, &h), if(h>lim, break); listput(v, [h, middle, small]); ); ); ); v = vecsort(Vec(v)); apply(f, v); }

Crossrefs

Cf. A176774, A176775, A342491.

Cf. A090466, A090467.

Sequence in context: A052119 A021593 A371134 * A019696 A119801 A191608

Adjacent sequences: A344080 A344081 A344082 * A344084 A344085 A344086

Keyword

nonn

Author

Michel Marcus, May 09 2021

Status

approved