A212595 Let f(n) = 2n-7. Difference between f(n) and the nearest prime < f(n).

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

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:

Mathematica

Array[# - Prime@ PrimePi[# - 1] &[2 # - 7] &, 86, 10] (* Michael De Vlieger, Oct 17 2019 *)
#-NextPrime[#, -1]&/@(2Range[7, 150]-7) (* Harvey P. Dale, Feb 03 2025 *)

Crossrefs

Sequence in context: A069177 A077659 A367953 * A087692 A093621 A242734

Adjacent sequences: A212592 A212593 A212594 * A212596 A212597 A212598

Keyword

nonn

Author

Michel Lagneau, May 22 2012

Status

approved