Revision History for A219389
(Underlined text is an addition;
strikethrough text is a deletion.)
Showing entries 1-10
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#39 by Michel Marcus at Tue Mar 15 04:35:52 EDT 2022
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#38 by Joerg Arndt at Tue Mar 15 03:49:49 EDT 2022
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#37 by Amiram Eldar at Tue Mar 15 03:48:52 EDT 2022
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#36 by Amiram Eldar at Tue Mar 15 03:38:18 EDT 2022
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| FORMULA
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Sum_{n>=2} 1/a(n) = 13/4 - cot(2*Pi/13)*Pi/2. - Amiram Eldar, Mar 15 2022
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| PROG
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(MAGMAMagma) [n: n in [0..7000] | IsSquare(13*n+1)];
(MAGMAMagma) I:=[0, 11, 15, 48, 56]; [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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approved
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#35 by Bruno Berselli at Thu Dec 01 03:18:11 EST 2016
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#34 by Bruno Berselli at Thu Dec 01 03:18:08 EST 2016
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| NAME
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Numbers nk such that 13*nk+1 is a square.
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| COMMENTS
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Equivalently, numbers of the form m*(13*m(13m+2), where m = 0,-1,1,-2,2,-3,3,...
Also, integer values of h(*(h+2)/13.
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approved
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#33 by Bruno Berselli at Thu Jan 07 04:45:39 EST 2016
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#32 by Bruno Berselli at Thu Jan 07 04:45:35 EST 2016
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| NAME
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Numbers n such that 13n13*n+1 is a square.
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approved
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#31 by Bruno Berselli at Tue Aug 11 04:31:25 EDT 2015
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#30 by Bruno Berselli at Tue Aug 11 04:31:16 EDT 2015
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| CROSSREFS
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Cf. numbers n such that k*n+1 is a square: A005563 (k=1), A046092 (k=2), A001082 (k=3), A002378 (k=4), A036666 (k=5), A062717 (k=6), A132354 (k=7), A000217 (k=8), A132355 (k=9), A132356 (k=10), A219257 (k=11), A152749 (k=12), A219390 (k=14), A204221 (k=15), A074378 (k=16), A219394 (k=17), A219395 (k=18), A219396 (k=19), A219190 (k=20), A219391 (k=21), A219392 (k=22), A219393 (k=23), A001318 (k=24), A219259 (k=25), A217441 (k=26), A219258 (k=27), A219191 (k=28).
Cf. similar sequences listed in A219257.
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approved
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