

A212595


Let f(n) = 2n7. Difference between f(n) and the nearest prime < f(n).


1



2, 2, 4, 2, 2, 4, 2, 4, 6, 2, 2, 4, 6, 2, 4, 2, 2, 4, 2, 4, 6, 2, 4, 6, 2, 2, 4, 6, 2, 4, 2, 2, 4, 6, 2, 4, 2, 4, 6, 2, 4, 6, 8, 2, 4, 2, 2, 4, 2, 2, 4, 2, 4, 6, 8, 10, 12, 14, 2, 4, 2, 4, 6, 2, 2, 4, 6, 8, 10, 2, 2, 4, 6, 2, 4, 6, 2, 4, 2, 4, 6, 2, 4, 6, 2, 2
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OFFSET

10,1


COMMENTS

It's known that there is always a prime between n and 2n  7 for all n >= 10.


LINKS

Michel Lagneau, Table of n, a(n) for n = 10..10000
Peter Vandendriessche and Hojoo Lee, Problems in elementary number theory, Problem E37


EXAMPLE

a(12) = 4 because 2*127 = 17, and the nearest prime p < 17 such that 12 < p < 17 is p = 13. Hence a(12) = 17  13 = 4.


MAPLE

with(numtheory):for n from 10 to 100 do:x:=2*n7:i:=0:for p from x1 by 1 to n+1 while(i=0) do:if type(p, prime)=true then i:=1:printf(`%d, `, xp):else fi:od:od:


MATHEMATICA

Array[#  Prime@ PrimePi[#  1] &[2 #  7] &, 86, 10] (* Michael De Vlieger, Oct 17 2019 *)


CROSSREFS

Sequence in context: A247257 A069177 A077659 * A087692 A093621 A242734
Adjacent sequences: A212592 A212593 A212594 * A212596 A212597 A212598


KEYWORD

nonn


AUTHOR

Michel Lagneau, May 22 2012


STATUS

approved



