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A051701

Closest prime to n-th prime p that is different from p (break ties by taking the smaller prime).

3, 2, 3, 5, 13, 11, 19, 17, 19, 31, 29, 41, 43, 41, 43, 47, 61, 59, 71, 73, 71, 83, 79, 83, 101, 103, 101, 109, 107, 109, 131, 127, 139, 137, 151, 149, 151, 167, 163, 167, 181, 179, 193, 191, 199, 197, 199, 227, 229, 227, 229, 241, 239, 257, 251, 257, 271, 269

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OFFSET

1,1

COMMENTS

A227878 gives the terms occurring twice. - Reinhard Zumkeller, Oct 25 2013

LINKS

T. D. Noe, Table of n, a(n) for n = 1..1000

EXAMPLE

Closest primes to 2,3,5,7,11 are 3,2,3,5,13.

MATHEMATICA

a[n_] := (p = Prime[n]; np = NextPrime[p]; pp = NextPrime[p, -1]; If[np-p < p-pp, np, pp]); Table[a[n], {n, 1, 58}] (* Jean-François Alcover, Oct 20 2011 *)

cp[{a_, b_, c_}]:=If[c-b<b-a, c, a]; Join[{3}, cp/@Partition[Prime[Range[ 60]], 3, 1]] (* Harvey P. Dale, Oct 08 2012 *)

PROG

(Haskell)

a051701 n = a051701_list !! (n-1)

a051701_list = f 2 $ 1 : a000040_list where

f d (q:ps@(p:p':_)) = (if d <= d' then q else p') : f d' ps

where d' = p' - p

-- Reinhard Zumkeller, Oct 25 2013

(Python)

from sympy import nextprime

def aupton(terms):

prv, cur, nxt, alst = 0, 2, 3, []