A076821 Squares of the differences between consecutive primes.

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

Offset

1,2

Comments

The sum of reciprocals is likely divergent, especially if the twin-prime 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