A157502 Even numbers without the squares.

2, 6, 8, 10, 12, 14, 18, 20, 22, 24, 26, 28, 30, 32, 34, 38, 40, 42, 44, 46, 48, 50, 52, 54, 56, 58, 60, 62, 66, 68, 70, 72, 74, 76, 78, 80, 82, 84, 86, 88, 90, 92, 94, 96, 98, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 122, 124, 126, 128, 130

Offset: 1

Author

Gerald Hillier, Mar 01 2009

Keywords

• nonn

Comments

Complement of A128201.

Examples

			a(2) = 6 as the next even after 2, i.e., 4 (a perfect square), drops out and is replaced by following even.
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A088828, A128201, A157512.

Cf. A000290 (squares), A005843 (even numbers).

Programs

Mathematica

Select[Range[2, 130, 2], ! IntegerQ@ Sqrt[#] &] (* Michael De Vlieger, Oct 01 2021 *)

PARI

isok(n) = ((n % 2) == 0) && ! issquare(n); \\ Michel Marcus, Aug 26 2013

Python

from math import isqrt
def A157502(n): return (k:=n<<1)+(r:=(m:=isqrt(k))+int((k-m*(m+1)<<2)>=1))-(r&1) # Chai Wah Wu, Jul 30 2022

Formula

Set R(n) = round(sqrt(2*n)), then a(n) = 2*n + R(n) - (R(n) mod 2).

Extensions

More terms from Michel Marcus, Aug 26 2013