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A060272 Distance from n^2 to closest prime.

%I A060272 #19 Jun 26 2021 15:30:31
%S A060272 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,
%T A060272 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,
%U A060272 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
%N A060272 Distance from n^2 to closest prime.
%H A060272 Michael De Vlieger, <a href="/A060272/b060272.txt">Table of n, a(n) for n = 1..10000</a>
%F A060272 a(n) = abs(A000290(n) - A113425(n)) = abs(A000290(n) - A113426(n)). - _Reinhard Zumkeller_, Oct 31 2005
%e A060272 n=1: n^2=1 has next prime 2, so a(1)=1;
%e A060272 n=11: n^2=121 is between primes {113,127} and closer to 127, thus a(11)=6.
%p A060272 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
%t A060272 Table[Function[k, Min[k - #, NextPrime@ # - k] &@ If[n == 1, 0, Prime@ PrimePi@ k]][n^2], {n, 103}] (* _Michael De Vlieger_, Jul 15 2017 *)
%t A060272 Min[#-NextPrime[#,-1],NextPrime[#]-#]&/@(Range[110]^2) (* _Harvey P. Dale_, Jun 26 2021 *)
%o A060272 (PARI) 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
%Y A060272 Cf. A007491, A053001, A058043, A056927, A053000, A051700, A060268-A060269, A060272, A059959, A059790.
%K A060272 nonn
%O A060272 1,3
%A A060272 _Labos Elemer_, Mar 23 2001