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A230389 Least k such that n! + k^2 + k is a perfect square. 1
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 (list; graph; refs; listen; history; text; internal format)
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
Sequence in context: A180403 A343582 A267512 * A048885 A264738 A002208
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

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Last modified March 5 05:51 EST 2024. Contains 370537 sequences. (Running on oeis4.)