

A054271


Difference between prime(n)^2 and the previous prime.


11



1, 2, 2, 2, 8, 2, 6, 2, 6, 2, 8, 2, 12, 2, 2, 6, 12, 2, 6, 2, 6, 12, 6, 2, 6, 8, 2, 2, 14, 6, 2, 2, 12, 2, 8, 14, 18, 8, 6, 2, 12, 12, 2, 6, 6, 20, 2, 2, 8, 8, 2, 2, 8, 12, 2, 6, 8, 8, 12, 20, 12, 2, 20, 18, 2, 6, 14, 2, 8, 12, 8, 2, 6, 6, 12, 6, 18, 30, 12, 12, 18, 2, 8, 12, 24, 2, 2, 6, 14, 6
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OFFSET

1,2


COMMENTS

From JeanChristophe 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 JeanChristophe Hervé, Oct 21 2013


EXAMPLE

n=4 and p(4)^2=49, preceded by p(15)=47, so a(4)=4947=2; n=97 and p(97)^2=509^2=259081, preceded by p(22765)=259033, so a(97)=259081259033=48.  Zak Seidov, Feb 20 2012


MATHEMATICA

f[n_]:=Module[{n2=n^2}, n2NextPrime[n2, 1]]; f/@Prime[Range[90]] (* Harvey P. Dale, Oct 19 2011 *)


CROSSREFS

Cf. A001248, A054270, A091666, A133517, A133518, A133519, A133520, A133521, A133522, A001223.
Sequence in context: A137508 A055921 A029605 * A278245 A240284 A011202
Adjacent sequences: A054268 A054269 A054270 * A054272 A054273 A054274


KEYWORD

nonn,easy


AUTHOR

Labos Elemer, May 05 2000


STATUS

approved



