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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 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

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