A113426 -id:A113426 - cp's OEIS frontend

A060272 Distance from n^2 to closest prime.

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

A113425 Smallest prime closest to n^2.

Original entry on oeis.org

2, 3, 7, 17, 23, 37, 47, 61, 79, 101, 127, 139, 167, 197, 223, 257, 293, 317, 359, 401, 439, 487, 523, 577, 619, 677, 727, 787, 839, 907, 967, 1021, 1087, 1153, 1223, 1297, 1367, 1447, 1523, 1601, 1669, 1759, 1847, 1933, 2027, 2113, 2207, 2309, 2399, 2503

Offset: 1

Reinhard Zumkeller, Oct 31 2005

nonn

A060272(n) = abs(A000290(n) - a(n));

a(n) <= A113426(n).

Robert Israel, Table of n, a(n) for n = 1..10000

f:= proc(n) local k,d;
  for k from 1 do
    for d in [-1,1] do
      if isprime(n^2 + k*d) then return n^2 + k*d fi
  od od
end proc:
map(f, [$1..100]); # Robert Israel, Mar 10 2017

sp[n_]:=Module[{n2=n^2 ,npu,npd},npu=NextPrime[n2]; npd=NextPrime[n2,-1]; If[n2-npd<=npu-n2,npd,npu]]; sp/@Range[50]  (* Harvey P. Dale, Feb 05 2011 *)

A181758 Greatest prime closest to n^3.

Original entry on oeis.org

2, 7, 29, 67, 127, 211, 347, 509, 727, 997, 1327, 1733, 2203, 2741, 3373, 4099, 4909, 5827, 6857, 7993, 9257, 10651, 12163, 13829, 15629, 17579, 19681, 21961, 24391, 26993, 29789, 32771, 35933, 39301, 42863, 46663, 50651, 54869, 59333, 63997, 68917, 74093, 79493, 85193, 91127, 97327, 103813, 110597, 117643, 125003

Offset: 1

Harvey P. Dale

nonn

			29 is the greatest prime closest to 3^3 = 27.

David A. Corneth, Table of n, a(n) for n = 1..10000

Cf. A113426.

f3[n_]:=Module[{n3=n^3,np1,np2},np1=NextPrime[n3,-1];np2=NextPrime[n3];If[(n3-np1)<(np2-n3),np1,np2]];
Table[f3[i],{i,50}]

a(n) = {if(n == 1, return(1)); my(n3 = n^3, gp = nextprime(n^3), lp = precprime(n^3)); if(n3 - lp < gp - n3, return(lp) , return(gp) ) } \\ David A. Corneth, May 25 2021

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A060272 Distance from n^2 to closest prime.

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A113425 Smallest prime closest to n^2.

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A181758 Greatest prime closest to n^3.

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