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 A076821 #16 Sep 08 2022 08:45:07 %S A076821 1,4,4,16,4,16,4,16,36,4,36,16,4,16,36,36,4,36,16,4,36,16,36,64,16,4, %T A076821 16,4,16,196,16,36,4,100,4,36,36,16,36,36,4,100,4,16,4,144,144,16,4, %U A076821 16,36,4,100,36,36,36,4,36,16,4,100,196,16,4,16,196,36,100,4,16,36,64,36 %N A076821 Squares of the differences between consecutive primes. %C A076821 The sum of reciprocals is likely divergent, especially if the twin-prime conjecture is true. %C A076821 The sum of the reciprocals diverges. In particular, the sum of the reciprocals up to n is at least n/(log n + log log n)^2 for n > 3. - _Charles R Greathouse IV_, Apr 17 2012 %H A076821 Vincenzo Librandi, <a href="/A076821/b076821.txt">Table of n, a(n) for n = 1..1000</a> %H A076821 B. Apostol, L. Panaitopol, L Petrescu, L. Toth, <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Toth/toth21.html">Some Properties of a Sequence Defined with the Aid of Prime Numbers</a>, J. Int. Seq. 18 (2015) # 15.5.5. %t A076821 Table[(Prime[n + 1] - Prime[n])^2, {n, 80}] (* _Vincenzo Librandi_, Jun 08 2016 *) %o A076821 (PARI) a(n)=(prime(n+1)-prime(n))^2 \\ _Charles R Greathouse IV_, Apr 17 2012 %o A076821 (Magma) [(NthPrime(n+1)-NthPrime(n))^2: n in [1..80]]; // _Vincenzo Librandi_, Jun 08 2016 %K A076821 easy,nonn %O A076821 1,2 %A A076821 _Cino Hilliard_, Nov 19 2002 %E A076821 Edited by _Don Reble_, May 03 2006