A342491 - OEIS

%I #22 May 08 2021 15:03:38

%S 12,14,23,12,28,29,27,20,38,52,27,22,11,47,20,49,53,16,69,81,17,47,59,

%T 59,34,41,93,32,76,33,34,121,76,93,88,33,37,39,101,102,83,27,90,52,73,

%U 183,75,37,45,130,105,15,155,83,120,54,106,133,129,15,123,42,225

%N 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)=A176774(m) is the smallest polygonality of m.

%C Inspired by (A245646, A245647, A245648), for which a(n) = 12.

%C Examples of lower terms: 11 for (21, 28, 35), 10 for (64, 120, 136) and 9 for (8778, 10296, 13530).

%H Michel Marcus, <a href="/A342491/b342491.txt">Table of n, a(n) for n = 1..12471</a> (hypotenuses <= 10000).

%F a(n) = f(A046083(n)) + f(A046084(n)) + f(A009000(n)) where f is A176774.

%e a(1) = 12 because (3, 4, 5) are (3-, 4-, 5-) gonal numbers, and 3+4+5=12.

%o (PARI) tp(n) = my(k=3); while( !ispolygonal(n,k), k++); k; \\ A176774

%o f(v) = vecsum(apply(tp, v));

%o 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);} \\ adapted from A009000

%Y Cf. A009000, A046083, A046084, A176774.

%Y Cf. A213188 (see 2nd comment).

%Y Cf. A245646, A245647, A245648.

%K nonn

%O 1,1

%A _Michel Marcus_, Mar 14 2021