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#33 by Charles R Greathouse IV at Thu Sep 08 08:44:34 EDT 2022
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(MAGMAMagma) [Floor((n+1)*Sqrt(2)+1/2) - Floor(n*Sqrt(2)+1/2): n in [1..30]]; // G. C. Greubel, Nov 18 2017
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Discussion
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| Thu Sep 08
| 08:44
| OEIS Server: https://oeis.org/edit/global/2944
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#32 by Harvey P. Dale at Fri Dec 10 19:29:46 EST 2021
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#31 by Harvey P. Dale at Fri Dec 10 19:29:42 EST 2021
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Differences[Table[Floor[n Sqrt[2]+1/2], {n, 120}]] (* Harvey P. Dale, Dec 10 2021 *)
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approved
editing
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#30 by Susanna Cuyler at Sat Nov 18 20:55:39 EST 2017
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#29 by Jon E. Schoenfield at Sat Nov 18 20:17:16 EST 2017
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#28 by Jon E. Schoenfield at Sat Nov 18 20:17:11 EST 2017
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An "eta-sequence": [ (": floor((n+1)*sqrt(2) + () + 1/2) ] - [ ) - floor(n*sqrt(2) + () + 1/2) ].).
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Presumably this is the same as the following sequence from Hofstadter's book: the number of triangular numbers between each successive pair of squares. More precisely, a(n) is the number of triangular numbers T such that n^2 <= T < (n+1)^2. E.g. ., a(3) = 2 because 3^2 <= T < 4^2 permits T(4) = 10 and T(5) = 15 and no other triangular number. - Hugo van der Sanden, May 03 2005.
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proposed
editing
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#27 by G. C. Greubel at Sat Nov 18 17:52:27 EST 2017
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#26 by G. C. Greubel at Sat Nov 18 17:51:57 EST 2017
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| FORMULA
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a(n) = floor((n+1)*sqrt(2) + 1/2) - floor(n*sqrt(2) + 1/2). - G. C. Greubel, Nov 18 2017
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(PARI) for(n=1, 30, print1(floor((n+1)*sqrt(2) + 1/2) - floor(n*sqrt(2) + 1/2), ", ")) \\ G. C. Greubel, Nov 18 2017
(MAGMA) [Floor((n+1)*Sqrt(2)+1/2) - Floor(n*Sqrt(2)+1/2): n in [1..30]]; // G. C. Greubel, Nov 18 2017
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approved
editing
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#25 by Bruno Berselli at Tue Nov 24 09:48:58 EST 2015
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#24 by Joerg Arndt at Tue Nov 24 09:02:10 EST 2015
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