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 A063657 Numbers with property that truncated square root is unequal to rounded square root. 5
 3, 7, 8, 13, 14, 15, 21, 22, 23, 24, 31, 32, 33, 34, 35, 43, 44, 45, 46, 47, 48, 57, 58, 59, 60, 61, 62, 63, 73, 74, 75, 76, 77, 78, 79, 80, 91, 92, 93, 94, 95, 96, 97, 98, 99, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120, 133, 134, 135, 136, 137, 138, 139, 140 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Also: skip 1, take 0, skip 2, take 1, skip 3, take 2, ... Integers for which the periodic part of the continued fraction for the square root of n begins with a 1. - Robert G. Wilson v, Nov 01 2001 a(n) belongs to the sequence iff a(n) > floor(sqrt(a(n))) * ceiling(sqrt(a(n))), i.e. a(n) in (k*(k+1),k^2), k >= 0. - Daniel Forgues, Apr 17 2011 LINKS Harry J. Smith, Table of n, a(n) for n=1,...,1000 MATHEMATICA Select[ Range[200], Floor[ Sqrt[ # ]] != Floor[ Sqrt[ # ] + 1/2] & ] or Select[ Range[200], First[ Last[ ContinuedFraction[ Sqrt[ # ]]]] == 1 & ] PROG (PARI) { n=0; for (m=0, 10^9, if (sqrt(m)%1 > .5, write("b063657.txt", n++, " ", m); if (n==1000, break)) ) } [From Harry J. Smith, Aug 27 2009] CROSSREFS Cf. A063656, A004201-A004202, A002620, A189151. Sequence in context: A028972 A153030 A031425 * A108575 A153219 A215034 Adjacent sequences:  A063654 A063655 A063656 * A063658 A063659 A063660 KEYWORD nonn AUTHOR Floor van Lamoen (fvlamoen(AT)hotmail.com), Jul 24 2001 STATUS approved

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