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A212595 Let f(n) = 2n-7. 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 (list; graph; refs; listen; history; text; internal format)
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*12-7 = 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*n-7:i:=0:for p from x-1 by -1 to n+1 while(i=0) do:if type(p, prime)=true then i:=1:printf(`%d, `, x-p):else fi:od:od:

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

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Last modified August 17 22:32 EDT 2018. Contains 313817 sequences. (Running on oeis4.)