A342491 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.

12, 14, 23, 12, 28, 29, 27, 20, 38, 52, 27, 22, 11, 47, 20, 49, 53, 16, 69, 81, 17, 47, 59, 59, 34, 41, 93, 32, 76, 33, 34, 121, 76, 93, 88, 33, 37, 39, 101, 102, 83, 27, 90, 52, 73, 183, 75, 37, 45, 130, 105, 15, 155, 83, 120, 54, 106, 133, 129, 15, 123, 42, 225

Offset

1,1

Comments

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

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

Links

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

Formula

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

Example

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

Prog

(PARI) tp(n) = my(k=3); while( !ispolygonal(n, k), k++); k; \\ A176774
f(v) = vecsum(apply(tp, 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); } \\ adapted from A009000

Crossrefs

Cf. A009000, A046083, A046084, A176774.

Cf. A213188 (see 2nd comment).

Cf. A245646, A245647, A245648.

Sequence in context: A342814 A255842 A229966 * A101557 A019292 A175886

Adjacent sequences: A342488 A342489 A342490 * A342492 A342493 A342494

Keyword

nonn

Author

Michel Marcus, Mar 14 2021

Status

approved