A230389 Least k such that n! + k^2 + k is a perfect square.

0, 0, 1, 5, 3, 119, 719, 260, 180, 495, 3628799, 39916799, 6561647, 9899, 722799, 15308432, 735092, 779904000, 1193692724, 77841862127, 1947879910469375, 7981643124, 231453720692, 37427202522827, 1793894810624, 251579908188224, 286527829489835787, 33866880878997899

Offset

0,4

Comments

a(n) <= n!-1, because with k=n!-1 we have n!+k^2+k = n! + (n!)^2 - 2*n! + 1 + n! - 1 = (n!)^2, a perfect square.

Links

Jon E. Schoenfield, Table of n, a(n) for n = 0..42

Example

4! + 3^2+3 = 24+12 = 36, a perfect square, so a(4)=3.

Crossrefs

Cf. A000290, A000142, A002378.

Sequence in context: A180403 A343582 A267512 * A048885 A264738 A002208

Adjacent sequences: A230386 A230387 A230388 * A230390 A230391 A230392

Keyword

nonn

Author

Alex Ratushnyak, Oct 18 2013

Extensions

a(18)-a(21) from Jon E. Schoenfield, Oct 24 2013

a(22) from Jon E. Schoenfield, Oct 26 2013

a(23) from Jon E. Schoenfield, Oct 29 2013

More terms from Jon E. Schoenfield, Nov 26 2013

Status

approved