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#34 by Michel Marcus at Wed Mar 16 05:49:37 EDT 2022
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#33 by Joerg Arndt at Wed Mar 16 04:57:18 EDT 2022
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#32 by Amiram Eldar at Wed Mar 16 04:24:11 EDT 2022
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#31 by Amiram Eldar at Wed Mar 16 04:15:08 EDT 2022
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| PROG
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(MAGMAMagma) [n: n in [0..11000] | IsSquare(22*n+1)];
(MAGMAMagma) I:=[0, 20, 24, 84, 92]; [n le 5 select I[n] else Self(n-1)+2*Self(n-2)-2*Self(n-3)-Self(n-4)+Self(n-5): n in [1..50]]; // Vincenzo Librandi, Aug 18 2013
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#30 by Amiram Eldar at Wed Mar 16 04:14:53 EDT 2022
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| FORMULA
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Sum_{n>=2} 1/a(n) = 11/2 - cot(Pi/11)*Pi/2. - Amiram Eldar, Mar 16 2022
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| STATUS
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approved
editing
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#29 by Bruno Berselli at Thu Dec 01 03:19:52 EST 2016
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#28 by Bruno Berselli at Thu Dec 01 03:19:49 EST 2016
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| NAME
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Numbers nk such that 22*nk+1 is a square.
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| STATUS
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approved
editing
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#27 by Bruno Berselli at Thu Jan 07 04:54:59 EST 2016
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#26 by Bruno Berselli at Thu Jan 07 04:54:56 EST 2016
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| NAME
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Numbers n such that 22n22*n+1 is a square.
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| COMMENTS
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Equivalently, numbers of the form m*(22*m(22m+2), where m = 0,-1,1,-2,2,-3,3,...
Also, integer values of 2h(2*h*(h+1)/11.
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| FORMULA
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G.f.: 4*x^2*(5+ + x+ + 5*x^2)/((1+ + x)^2*(1- - x)^3).
a(n) = a(-n+1) = (22*n*(n-1)+) + 9*(-1)^n*(2*n- - 1)+) + 1)/4 + + 2.
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| STATUS
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approved
editing
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#25 by Bruno Berselli at Tue Aug 11 04:36:36 EDT 2015
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