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

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

MATHEMATICA

f[n_]:=Module[{n2=n^2}, n2-NextPrime[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

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Last modified August 17 15:28 EDT 2018. Contains 313816 sequences. (Running on oeis4.)