A372630 Numbers k with property that there exists an m>k such that the sum of the natural numbers from k^2 to m^2 inclusive is a square number.

1, 3, 8, 11, 12, 14, 17, 23, 30, 33, 35, 37, 41, 48, 59, 60, 65, 68, 77, 79, 82, 84, 89, 93, 94, 99

Offset

1,2

Links

Table of n, a(n) for n=1..26.

Nicolay Avilov, Problem 1876. Segment of a natural series (in Russian).

Example

The number 3 is a member of the sequence because the sum of all natural numbers from 3^2 to 4^2 inclusive is 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 = 100, with 100 = 10^2.

Prog

(PARI) check(k, mm=100) = my(d=2*k^2-1, v=List([]), x, y, z); for(t=d+1, 17*d, if(issquare((t^2-d^2)/2), listput(v, t))); if(v[#v\2] != 3*d, return(-1)); for(i=1, #v\2, x=v[i]; y=v[i+#v\2]; for(j=1, mm, if(issquare((x-1)/2) && x>d+2, return(1)); z=6*y-x; x=y; y=z)); 0; \\ Jinyuan Wang, Jul 06 2024; just for checking

Crossrefs

Cf. A000290, A372631, A373330.

Sequence in context: A305176 A046545 A279585 * A350395 A108752 A310279

Adjacent sequences: A372627 A372628 A372629 * A372631 A372632 A372633

Keyword

nonn,more

Author

Nicolay Avilov, May 07 2024

Status

approved