A059959 -id:A059959 - cp's OEIS frontend

A117387 Prime nearest to 2^n. In case of a tie, choose the smaller.

2, 2, 3, 7, 17, 31, 61, 127, 257, 509, 1021, 2053, 4093, 8191, 16381, 32771, 65537, 131071, 262147, 524287, 1048573, 2097143, 4194301, 8388617, 16777213, 33554467, 67108859, 134217757, 268435459, 536870909, 1073741827, 2147483647, 4294967291, 8589934583

Offset: 0

Lekraj Beedassy, Mar 11 2006

nonn

Harvey P. Dale, Table of n, a(n) for n = 0..1000

f[n_] := Block[{k = 0}, While[ !PrimeQ[2^n - k] && !PrimeQ[2^n + k], k++ ]; Min@Select[{2^n - k, 2^n + k}, PrimeQ@# &]]
pn2n[n_]:=Module[{c=2^n,a,b},a=NextPrime[c,-1];b=NextPrime[c];If[b-c < c-a,b,a]]; Join[{2,2},Table[pn2n[n],{n,2,40}]] (* Harvey P. Dale, Jul 24 2019 *)

from sympy import prevprime, nextprime
def A117387(n): return (m if (m:=nextprime(k:=1<1 else 2 # Chai Wah Wu, Aug 08 2022

a(n) = A000079(n) - A059959(n). [Corrected by Georg Fischer, Dec 13 2022]

Edited, corrected and extended by Robert G. Wilson v, Mar 14 2006

A060268 Distance of 2n from the closest prime.

Original entry on oeis.org

1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 3, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 3, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 3, 5, 7, 5, 3, 1, 1, 1, 1, 3, 1, 1, 1, 3, 5, 3, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 1, 3, 1, 1, 3, 1, 1, 1, 3, 5, 3, 1, 1, 1, 1, 1, 1, 3, 5, 5, 3, 1, 1

Offset: 2

Labos Elemer, Mar 23 2001

nonn

			n=13, 2n=26 surrounded by 23 and 29 which are from 26 in equal distance of 3 and min{3,3}=3=a(13).

Cf. A020482, A049653, A051702, A059959, A060266.

with(numtheory): [seq(min(nextprime(2*i)-2*i, 2*i-prevprime(2*i)), i=2...256)];

a[n_] := Min[NextPrime[2*n] - 2*n, 2*n - NextPrime[2*n, -1]]; Array[a, 100, 2] (* Amiram Eldar, Sep 16 2020 *)

a(n) = min(2*n - precprime(2*n-1), nextprime(2*n+1) - 2*n); \\ Michel Marcus, Sep 16 2020

a(n) = min(A049653(n), A060266(n)). - Michel Marcus, Sep 16 2020

A060272 Distance from n^2 to closest prime.

Original entry on oeis.org

1, 1, 2, 1, 2, 1, 2, 3, 2, 1, 6, 5, 2, 1, 2, 1, 4, 7, 2, 1, 2, 3, 6, 1, 6, 1, 2, 3, 2, 7, 6, 3, 2, 3, 2, 1, 2, 3, 2, 1, 12, 5, 2, 3, 2, 3, 2, 5, 2, 3, 8, 3, 6, 1, 2, 1, 2, 3, 10, 7, 2, 3, 2, 3, 4, 1, 4, 3, 2, 3, 2, 5, 4, 1, 2, 3, 2, 5, 6, 3, 2, 5, 6, 1, 4, 3, 4, 3, 2, 1, 6, 3, 2, 1, 4, 5, 4, 3, 2, 7, 8, 5, 2

Offset: 1

Labos Elemer, Mar 23 2001

nonn

			n=1: n^2=1 has next prime 2, so a(1)=1;
n=11: n^2=121 is between primes {113,127} and closer to 127, thus a(11)=6.

Michael De Vlieger, Table of n, a(n) for n = 1..10000

Cf. A007491, A053001, A058043, A056927, A053000, A051700, A060268-A060269, A060272, A059959, A059790.

seq((s-> min(nextprime(s)-s, `if`(s>2, s-prevprime(s), [][])))(n^2), n=1..256);  # edited by Alois P. Heinz, Jul 16 2017

Table[Function[k, Min[k - #, NextPrime@ # - k] &@ If[n == 1, 0, Prime@ PrimePi@ k]][n^2], {n, 103}] (* Michael De Vlieger, Jul 15 2017 *)
Min[#-NextPrime[#,-1],NextPrime[#]-#]&/@(Range[110]^2) (* Harvey P. Dale, Jun 26 2021 *)

a(n) = if (n==1, nextprime(n^2) - n^2, min(n^2 - precprime(n^2), nextprime(n^2) - n^2)); \\ Michel Marcus, Jul 16 2017

a(n) = abs(A000290(n) - A113425(n)) = abs(A000290(n) - A113426(n)). - Reinhard Zumkeller, Oct 31 2005

cp's OEIS Frontend

A117387 Prime nearest to 2^n. In case of a tie, choose the smaller.

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A060268 Distance of 2n from the closest prime.

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A060272 Distance from n^2 to closest prime.

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