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.
%I A081115 #53 Dec 26 2019 05:09:35 %S A081115 2,4,10,14,24,30,44,70,80,114,140,154,184,234,290,310,374,420,444,520, %T A081115 574,660,784,850,884,954,990,1064,1344,1430,1564,1610,1850,1900,2054, %U A081115 2214,2324,2494,2670,2730,3040,3104,3234,3300,3710,4144,4294,4370,4524 %N A081115 (p^2 - 1)/12 where p > 3 runs through the primes. %C A081115 If p=4k+1, (p^2 - 1)/12 = Sum_{i=1..k} floor(sqrt(i*k)) (see links). - _R. J. Mathar_, Jul 07 2006 %C A081115 For n=1 and 2, the corresponding primes being 2 and 3, and a(n) is a fraction, not entered here. - _Michel Marcus_, Nov 11 2013 %C A081115 For prime p > 3, (p^2 - 1)/12 = (1/p)*Sum_{k=0..floor(p/2)} (p - k)*k. - _Joseph Wheat_, Feb 03 2018 %H A081115 Muniru A Asiru, <a href="/A081115/b081115.txt">Table of n, a(n) for n = 3..5000</a> %H A081115 Hojoo Lee, <a href="http://www.staff.science.uu.nl/~beuke106/getaltheorie/pen0795.pdf">Problems in Elementary Number Theory</a>, p. 14, problem 10. %H A081115 George Pólya and Gabor Szego, <a href="http://books.google.com/books?id=pCa2CmAt8pwC&printsec=frontcover&source=gbs_ge_summary_r&cad=0#v=onepage&q=%22prime%20number%20of%20the%20form%22&f=false">Problems and Theorems in Analysis II</a>, p. 113, problem 20. %H A081115 S. A. Shirali, <a href="http://www.jstor.org/stable/2690862">A family portrait of primes -- a case study in discrimination</a>, Math. Mag.. Vol. 70, No. 4 (Oct. 1997), pp. 263-272. %F A081115 a(n) = j*(j+1)/3 where A000040(n)=2*j+1. - _R. J. Mathar_, Jul 07 2006 %F A081115 a(n) = (A001248(n) - 1)/12. - _Vicente Izquierdo Gomez_, May 25 2013 %F A081115 a(n) = 2*A024702(n). - _R. J. Mathar_, Jan 09 2017 %F A081115 a(n) = (prime(n)^2 - 1)/12 for n >= 3. - _Jon E. Schoenfield_, Dec 25 2019 %p A081115 seq((ithprime(p)^2-1)/12, p=3..20); # _Muniru A Asiru_, Feb 04 2018 %t A081115 (Prime[Range[3, 51]]^2 - 1)/12 (* _Giovanni Resta_, May 25 2013 *) %o A081115 (PARI) a(n) = p = prime(n); (p^2-1)/12; \\ _Michel Marcus_, Nov 11 2013 %o A081115 (GAP) List(Filtered([5..20], IsPrime), p->(p^2-1)/12); # _Muniru A Asiru_, Feb 04 2018 %K A081115 nonn %O A081115 3,1 %A A081115 _Benoit Cloitre_, Apr 16 2003 %E A081115 Offset set to 3 and edited by _Michel Marcus_, Nov 11 2013