cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A005722 a(n) = (prime(n) - 1)^2.

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%I A005722 #32 May 08 2024 04:18:42
%S A005722 1,4,16,36,100,144,256,324,484,784,900,1296,1600,1764,2116,2704,3364,
%T A005722 3600,4356,4900,5184,6084,6724,7744,9216,10000,10404,11236,11664,
%U A005722 12544,15876,16900,18496,19044,21904,22500,24336,26244,27556,29584,31684,32400,36100
%N A005722 a(n) = (prime(n) - 1)^2.
%H A005722 Vincenzo Librandi, <a href="/A005722/b005722.txt">Table of n, a(n) for n = 1..1000</a>
%H A005722 Richard K. Guy, <a href="/A005712/a005712.pdf">Letter to N. J. A. Sloane, 1987</a>.
%F A005722 a(n) = A192134(A095874(A001248(n))) - 1. - _Reinhard Zumkeller_, Jun 26 2011
%F A005722 a(n) = A006093(n)^2. - _Wesley Ivan Hurt_, Mar 27 2014
%F A005722 Sum_{n>=1} 1/a(n) = A086242. - _Amiram Eldar_, Nov 09 2020
%F A005722 From _Amiram Eldar_, Jan 23 2021: (Start)
%F A005722 Product_{n>=1} (1 + 1/a(n)) = A065485.
%F A005722 Product_{n>=2} (1 - 1/a(n)) = A005597. (End)
%p A005722 A005722:=n->(ithprime(n)-1)^2; seq(A005722(n), n=1..40); # _Wesley Ivan Hurt_, Mar 27 2014
%t A005722 Table[(Prime[n] - 1)^2, {n, 40}] (* _Vincenzo Librandi_, Mar 27 2014 *)
%o A005722 (Magma) [(p-1)^2: p in PrimesUpTo(200)]; // _Vincenzo Librandi_, Mar 27 2014
%o A005722 (PARI) a(n) = (prime(n) - 1)^2; \\ _Michel Marcus_, Nov 09 2020
%Y A005722 Cf. A001248, A005597, A006093, A065485, A086242, A095874, A192134.
%K A005722 nonn,easy
%O A005722 1,2
%A A005722 Scorpion(AT)aol.com