

A076821


Squares of the differences between consecutive primes.


4



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, 16, 4, 16, 196, 16, 36, 4, 100, 4, 36, 36, 16, 36, 36, 4, 100, 4, 16, 4, 144, 144, 16, 4, 16, 36, 4, 100, 36, 36, 36, 4, 36, 16, 4, 100, 196, 16, 4, 16, 196, 36, 100, 4, 16, 36, 64, 36
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OFFSET

1,2


COMMENTS

The sum of reciprocals is likely divergent, especially if the twinprime conjecture is true.
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


LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..1000
B. Apostol, L. Panaitopol, L Petrescu, L. Toth, Some Properties of a Sequence Defined with the Aid of Prime Numbers, J. Int. Seq. 18 (2015) # 15.5.5.


MATHEMATICA

Table[(Prime[n + 1]  Prime[n])^2, {n, 80}] (* Vincenzo Librandi, Jun 08 2016 *)


PROG

(PARI) a(n)=(prime(n+1)prime(n))^2 \\ Charles R Greathouse IV, Apr 17 2012
(MAGMA) [(NthPrime(n+1)NthPrime(n))^2: n in [1..80]]; // Vincenzo Librandi, Jun 08 2016


CROSSREFS

Sequence in context: A135944 A268169 A177241 * A165825 A056959 A255300
Adjacent sequences: A076818 A076819 A076820 * A076822 A076823 A076824


KEYWORD

easy,nonn


AUTHOR

Cino Hilliard, Nov 19 2002


EXTENSIONS

Edited by Don Reble, May 03 2006


STATUS

approved



