A089237 List of primes and squares.

0, 1, 2, 3, 4, 5, 7, 9, 11, 13, 16, 17, 19, 23, 25, 29, 31, 36, 37, 41, 43, 47, 49, 53, 59, 61, 64, 67, 71, 73, 79, 81, 83, 89, 97, 100, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 144, 149, 151, 157, 163, 167, 169, 173, 179, 181, 191, 193, 196, 197, 199, 211, 223, 225, 227

Offset

1,3

Links

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

Formula

a(A161187(n)+1) = A000290(n); a(A161188(n)+1) = A000040(n). - Reinhard Zumkeller, Dec 18 2012

A010051(a(n)) + A010052(a(n)) = 1. - Reinhard Zumkeller, Jul 07 2014

a(n) ~ n log n. - Charles R Greathouse IV, Oct 14 2016

Mathematica

m=100; Sort[Flatten[{Range[0, m]^2, Prime[Range[PrimePi[m^2]]]}]] (* Zak Seidov, Nov 05 2009 *)

Prog

(Haskell)
a089237 n = a089237_list !! (n-1)
a089237_list = merge a000040_list a000290_list where
   merge xs'@(x:xs) ys'@(y:ys) =
         if x < y then x : merge xs ys' else y : merge xs' ys
-- Reinhard Zumkeller, Dec 18 2012
(PARI) is(n)=isprime(n) || issquare(n) \\ Charles R Greathouse IV, Oct 14 2016
(PARI) {A89237=List([0..5]); A089237(n)=while(#A89237<n, my(t=A89237[#A89237]); forprime(p=t+1, t=(sqrtint(t)+1)^2, listput(A89237, p)); listput(A89237, t)); A89237[n]} \\ For use in other functions, e.g., A340389. - M. F. Hasler, Jul 24 2021, edited Sep 01 2021

Crossrefs

Complement of A089229.

Cf. A010051, A010052.

Sequence in context: A123193 A345944 A066724 * A352870 A009087 A026477

Adjacent sequences: A089234 A089235 A089236 * A089238 A089239 A089240

Keyword

nonn

Author

N. J. A. Sloane, Dec 11 2003

Status

approved