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%I #16 Sep 08 2022 08:45:07
%S 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 16,4,16,196,16,36,4,100,4,36,36,16,36,36,4,100,4,16,4,144,144,16,4,
%U 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 Squares of the differences between consecutive primes.
%C The sum of reciprocals is likely divergent, especially if the twin-prime conjecture is true.
%C 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 Vincenzo Librandi, <a href="/A076821/b076821.txt">Table of n, a(n) for n = 1..1000</a>
%H 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 Table[(Prime[n + 1] - Prime[n])^2, {n, 80}] (* _Vincenzo Librandi_, Jun 08 2016 *)
%o (PARI) a(n)=(prime(n+1)-prime(n))^2 \\ _Charles R Greathouse IV_, Apr 17 2012
%o (Magma) [(NthPrime(n+1)-NthPrime(n))^2: n in [1..80]]; // _Vincenzo Librandi_, Jun 08 2016
%K easy,nonn
%O 1,2
%A _Cino Hilliard_, Nov 19 2002
%E Edited by _Don Reble_, May 03 2006
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