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

Author

Amarnath Murthy, Nov 12 2005

Keywords

• nonn

Comments

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

Examples

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

Crossrefs

Cf. A024675.

Programs

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

Extensions

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