A373328 Numbers k such that the difference between T = k*(k+1)/2 = A000217(k) and the largest square <= T reaches a new record.

0, 2, 5, 9, 12, 15, 19, 22, 29, 32, 39, 46, 53, 56, 63, 70, 73, 80, 87, 90, 97, 104, 111, 114, 121, 131, 155, 172, 189, 213, 230, 254, 271, 295, 312, 329, 353, 370, 394, 411, 428, 452, 469, 493, 510, 527, 551, 568, 592, 609, 633, 650, 667, 691, 708, 732, 749, 766

Offset

1,2

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Maple

J:= 0: m:= 0: count:= 1:
for i from 1 while count < 100 do
  t:= i*(i+1)/2;
  v:= t - floor(sqrt(t))^2;
  if v > m then
    J:= J, i; m:= v; count:= count+1;
   fi
od:
J; # Robert Israel, Dec 19 2024

Prog

(PARI) a373328(nmax) = {my(m=-oo); for(n=0, nmax, my(T=n*(n+1)/2, d=T-sqrtint(T)^2); if(d>m, print1(n, ", "); m=d))};
a373328(770)

Crossrefs

A373327 gives the corresponding differences.

Cf. A000217, A000290, A064784, A128549.

Sequence in context: A063957 A184579 A186274 * A184926 A342745 A189384

Adjacent sequences: A373325 A373326 A373327 * A373329 A373330 A373331

Keyword

nonn

Author

Hugo Pfoertner, Jun 01 2024

Status

approved