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

1,1

Comments

Complement of A128201.

Links

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

Formula

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

Example

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

Mathematica

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

Prog

(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

Crossrefs

Cf. A088828, A128201, A157512.

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

Sequence in context: A005795 A319827 A327905 * A216032 A076300 A049637

Adjacent sequences: A157499 A157500 A157501 * A157503 A157504 A157505

Keyword

nonn

Author

Gerald Hillier, Mar 01 2009

Extensions

More terms from Michel Marcus, Aug 26 2013

Status

approved