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URL: https://oeis.org/A051697

⇱ A051697 - OEIS

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A051697
Closest prime to n (break ties by taking the smaller prime).
25
2, 2, 2, 3, 3, 5, 5, 7, 7, 7, 11, 11, 11, 13, 13, 13, 17, 17, 17, 19, 19, 19, 23, 23, 23, 23, 23, 29, 29, 29, 29, 31, 31, 31, 31, 37, 37, 37, 37, 37, 41, 41, 41, 43, 43, 43, 47, 47, 47, 47, 47, 53, 53, 53, 53, 53, 53, 59, 59, 59, 59, 61, 61, 61, 61, 67, 67, 67, 67, 67, 71, 71
OFFSET
0,1
LINKS
Eric Weisstein's World of Mathematics, Nearest Prime
EXAMPLE
Closest primes to 0,1,2,3,4 are 2,2,2,3,3.
MATHEMATICA
a[n_] := (np = NextPrime[n]; pp = Prime[PrimePi[np] - 1]; Which[np > 2n-pp, pp, np < 2n-pp, np, True, pp]); a[0] = a[1] = 2; Table[a[n], {n, 0, 71}] (* Jean-François Alcover, Jul 28 2011 *)
PROG
(PARI) a(n)=if(n<3, return(2)); my(p=precprime(n), q=nextprime(n)); if(q-n<n-p, q, p) \\ Charles R Greathouse IV, Apr 28 2015
(Python)
from sympy import prevprime, nextprime
def A051697(n): return 2 if n<3 else p if (q:=nextprime(n-1))+(p:=prevprime(n+1))>=(n<<1) else q # Chai Wah Wu, Oct 25 2025
CROSSREFS
KEYWORD
nonn,easy
EXTENSIONS
More terms from James Sellers
STATUS
approved