A248170 Nonnegative integer whose square is the closest square to prime(n).

1, 2, 2, 3, 3, 4, 4, 4, 5, 5, 6, 6, 6, 7, 7, 7, 8, 8, 8, 8, 9, 9, 9, 9, 10, 10, 10, 10, 10, 11, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 13, 13, 14, 14, 14, 14, 15, 15, 15, 15, 15, 15, 16, 16, 16, 16, 16, 16, 17, 17, 17, 17, 18, 18, 18, 18, 18, 18, 19, 19, 19, 19, 19, 19, 19, 20, 20, 20

Offset

1,2

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Formula

a(n) = sqrt(A246934(n)).

Mathematica

ns[n_]:=Module[{s=Sqrt[n], a, b}, a=Floor[s]; b=Ceiling[s]; If[n-a^2<= b^2- n, a, b]]; ns/@Prime[Range[80]]
Sqrt[#]&/@With[{s=Range[20]^2}, Table[Nearest[s, p], {p, Prime[ Range[ PrimePi[ Max[s]]]]-1}]]//Flatten (* Harvey P. Dale, May 14 2020 *)

Prog

(PARI) {forprime (p = 2, 400, a = sqrtint (p); b = (a + 1)^2; a = a^2;
   s = if (b - p > p - a, a, b); print1 (sqrtint (s) ", "))}

Crossrefs

Cf. A000040, A246934.

Sequence in context: A000006 A061017 A331535 * A225545 A088462 A189574

Adjacent sequences: A248167 A248168 A248169 * A248171 A248172 A248173

Keyword

nonn

Author

Zak Seidov, Oct 03 2014

Status

approved