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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified February 22 09:55 EST 2019. Contains 320390 sequences. (Running on oeis4.)