A059790 -id:A059790 - 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

A060271 Difference between smallest prime following and largest prime preceding 2*(n-th prime).

Original entry on oeis.org

2, 2, 4, 4, 4, 6, 6, 4, 4, 6, 6, 6, 4, 6, 8, 4, 14, 14, 6, 10, 10, 6, 4, 6, 4, 12, 12, 12, 12, 4, 6, 6, 6, 4, 14, 14, 4, 14, 6, 10, 6, 8, 4, 6, 8, 4, 10, 6, 8, 4, 4, 12, 8, 4, 12, 18, 18, 6, 10, 6, 6, 10, 4, 12, 12, 10, 12, 4, 10, 10, 8, 10, 6, 8, 4, 8, 14, 10, 12, 10, 10, 14, 4, 14, 4, 4, 20, 8

Offset: 1

Labos Elemer, Mar 23 2001

nonn

			For n = 1: prime(1) = 2, 2*prime(1) = 4 is between 3 and 5, their difference is 2 = a(1).
For n = 6: prime(6) = 13, 2*prime(6) = 26 is between 23 and 29 and their difference is 6 = a(6).

Amiram Eldar, Table of n, a(n) for n = 1..10000

Cf. A059786, A059787, A059788, A059789, A059790, A013633, A058043, A058249, A058044, A060267, A001223.

with(numtheory): [seq(nextprime(2*ithprime(j))-prevprime(2*ithprime(j)),j=1...256)];

dsplp[n_]:=Module[{np=2Prime[n]},NextPrime[np]-NextPrime[np,-1]]; Array[ dsplp,90] (* Harvey P. Dale, Mar 20 2013 *)

a(n) = {my(m = 2*prime(n)); nextprime(m+1) - precprime(m-1);} \\ Amiram Eldar, Feb 08 2025

Offset changed to 1 and a(1) prepended by Amiram Eldar, Feb 08 2025

cp's OEIS Frontend

A060272 Distance from n^2 to closest prime.

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