A079666 Least k such that the distance from k^2 to closest prime = n or zero if no k exists.

1, 3, 8, 17, 12, 11, 18, 51, 200, 59, 238, 41, 276, 165, 104, 281, 214, 397, 348, 159, 650, 305, 778, 923, 2242, 1155, 1090, 911, 822, 1871, 1280, 1099, 1516, 3253, 2578, 5849, 3538, 693, 4010, 1937, 1284, 5095, 3212, 2011, 6268, 6331, 2160, 1943, 12470, 13443, 12836, 7405, 25428, 7115, 22596, 10873

Offset: 1

Author

Benoit Cloitre, Jan 26 2003

Keywords

• nonn

Comments

From Robert Israel, Jan 03 2017: (Start)

For n > 1, a(n) == n (mod 2) unless it is 0.

a(191) > 3*10^7 if it is not 0. (End)

Links

• Robert Israel, Table of n, a(n) for n = 1..190

Crossrefs

Cf. A051699, A060272.

Programs

Maple

N:= 100: # for a(1)..a(N)
R[1]:= 1: count:= 1:
for k from 3 while count < N do
d:= min(nextprime(k^2)-k^2,k^2-prevprime(k^2));
if d <= N and not assigned(R[d]) then R[d]:= k; count:= count+1 fi
od:
seq(R[i],i=1..N); # Robert Israel, Jan 03 2017

PARI

a(n)=if(n<0,0,s=1; while(abs(n-min(abs(precprime(s^2)-s^2),abs(nextprime(s^2)-s^2)))>0,s++); s)

Extensions

More terms from Robert Israel, Jan 03 2017