A114010 a(1) = a(2) = 2, Let k(n) = (prime(n) + prime(n+1))/2. Then a(k(n)) = k(n). a(k(n)-i) = prime(n), a(k(n)+i) = prime(n+1) until the next prime occurs.

2, 2, 3, 4, 5, 6, 7, 7, 9, 11, 11, 12, 13, 13, 15, 17, 17, 18, 19, 19, 21, 23, 23, 23, 23, 26, 29, 29, 29, 30, 31, 31, 31, 34, 37, 37, 37, 37, 39, 41, 41, 42, 43, 43, 45, 47, 47, 47, 47, 50, 53, 53, 53, 53, 53, 56, 59, 59, 59, 60, 61, 61, 61, 64, 67, 67, 67, 67, 69, 71, 71, 72

Offset

1,1

Comments

a(n) is the nearest prime to n, or n if there is a tie. - Wesley Ivan Hurt, May 15 2021

Links

Table of n, a(n) for n=1..72.

Example

(7 + 11)/2 = 9 hence a(9) = 9, a(8) = 7, a(7) = 7, a(10) = 11, a(11) = 11.

Maple

A114010 := proc(n) local i, a024675 ; if n <= 2 then 2 ; else for i from 1 do if n >= ithprime(i) and n <= ithprime(i+1) then a024675 := (ithprime(i)+ithprime(i+1))/2 ; if n = a024675 then RETURN(a024675) ; elif n < a024675 then RETURN(ithprime(i)) ; else RETURN(ithprime(i+1)) ; fi ; fi ; od: fi ; end: seq(A114010(n), n=1..120) ; # R. J. Mathar, Feb 06 2008

Crossrefs

Cf. A024675.

Sequence in context: A353212 A078171 A157282 * A289188 A111633 A273662

Adjacent sequences: A114007 A114008 A114009 * A114011 A114012 A114013

Keyword

nonn

Author

Amarnath Murthy, Nov 12 2005

Extensions

More terms from R. J. Mathar, Feb 06 2008

Status

approved