OFFSET
1,2
COMMENTS
From Jean-Christophe Hervé, Oct 22 2013: (Start)
Contains only even numbers, except the first term.
Even integers of the form 3*k+1 (or equivalently integers of form 6*k+4) never appear because prime(n)^2 = 3*k+1 = 1 (mod 3), and prime(n)^2 - (3*k+1) is multiple of 3.
Conjecture: every other even integer appears in the sequence an infinite number of times. (End)
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
FORMULA
a(n) = prime(n)^2 - precprime(prime(n)^2), where precprime(x) is the largest prime less than x. [Corrected by Jean-Christophe Hervé, Oct 21 2013]
EXAMPLE
From Zak Seidov, Feb 20 2012: (Start)
n=4 and prime(4)^2=49, preceded by prime(15)=47, so a(4)=49-47=2;
n=97 and prime(97)^2=509^2=259081, preceded by prime(22765)=259033, so a(97)=259081-259033=48. (End)
MATHEMATICA
f[n_]:=Module[{n2=n^2}, n2-NextPrime[n2, -1]]; f/@Prime[Range[90]] (* Harvey P. Dale, Oct 19 2011 *)
PROG
(PARI) a(n) = my(p=prime(n)); p^2 - precprime(p^2); \\ Michel Marcus, Feb 27 2023
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Labos Elemer, May 05 2000
STATUS
approved