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 A078358 Non-oblong numbers: Complement of A002378. 15
 1, 3, 4, 5, 7, 8, 9, 10, 11, 13, 14, 15, 16, 17, 18, 19, 21, 22, 23, 24, 25, 26, 27, 28, 29, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 73, 74 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS The (primitive) period length k(n)=A077427(n) of the (regular) continued fraction of (sqrt(4*a(n)+1)+1)/2 determines whether or not the Diophantine equation (2*x-y)^2 - (1+4*a(n))*y^2 = +4 or -4 is solvable and the approximants of this continued fraction give all solutions. See A077057. The following sequences all have the same parity: A004737, A006590, A027052, A071028, A071797, A078358, A078446. - Jeremy Gardiner, Mar 16 2003 Infinite series 1/A078358(n) is divergent. Proof: Harmonic series 1/A000027(n) is divergent and can be distributed on two subseries 1/A002378(k+1) and 1/A078358(m). Because infinite subseries 1/A002378(k+1) is convergent to 1 it means that Sum[1/A078358(n),{n,1,Infinity}] is divergent. [From Artur Jasinski, Sep 28 2008] REFERENCES O. Perron, "Die Lehre von den Kettenbruechen, Bd.I", Teubner, 1954, 1957 (Sec. 30, Satz 3.35, p. 109 and table p. 108). LINKS _Reinhard Zumkeller_, Table of n, a(n) for n = 1..10000 FORMULA 4*a(n)+1 is not a square number. a(n) = ceiling(squareroot(n)) + n -1. - Leroy Quet Jul 06 2007 MATHEMATICA Complement[Range[930], Table[n (n + 1), {n, 0, 30}]] (* and *) Table[Ceiling[Sqrt[n]] + n - 1, {n, 900}] (* From Vladimir Joseph Stephan Orlovsky, Jul 20 2011 *) PROG (Haskell) a078358 n = a078358_list !! (n-1) a078358_list = compl [0..] a002378_list where    compl (u:us) vs'@(v:vs) | u == v = compl us vs                            | u /= v = u : compl us vs' -- Reinhard Zumkeller, May 08 2012 (PARI) a(n)=sqrtint(n-1)+n \\ Charles R Greathouse IV, Jan 17 2013 CROSSREFS a(n)=(A077425(n)-1)/4. Cf. A049068 (subsequence), A144786. Sequence in context: A039177 A058986 A184431 * A175968 A152012 A173153 Adjacent sequences:  A078355 A078356 A078357 * A078359 A078360 A078361 KEYWORD nonn,easy AUTHOR Wolfdieter Lang, Nov 29 2002 STATUS approved

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