A176693 Union of squares and the even numbers.

0, 1, 2, 4, 6, 8, 9, 10, 12, 14, 16, 18, 20, 22, 24, 25, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 48, 49, 50, 52, 54, 56, 58, 60, 62, 64, 66, 68, 70, 72, 74, 76, 78, 80, 81, 82, 84, 86, 88, 90, 92, 94, 96, 98, 100, 102, 104, 106, 108, 110, 112, 114, 116, 118, 120, 121, 122

Offset: 1

Author

Vincenzo Librandi, Apr 24 2010

Keywords

• nonn
• easy

Comments

Numbers k such that k^k is a square. - Chai Wah Wu, Sep 18 2024

Crossrefs

Cf. A128201 (Union of squares and the odd numbers).

Programs

Mathematica

With[{upto=150},Union[Join[Range[0,upto,2],Range[Sqrt[upto]]^2]]] (* Harvey P. Dale, Apr 29 2015 *)

PARI

is_A176693(n)=!bittest(n, 0)||issquare(n) \\ M. F. Hasler, Apr 19 2015

Python

from math import isqrt
def A176693(n):
    def f(x): return n-1+(x>>1)+(x&1)-(isqrt(x)+1>>1)
    m, k = n-1, f(n-1)
    while m != k: m, k = k, f(k)
    return m # Chai Wah Wu, Sep 18 2024

Extensions

Initial a(1)=0 added by M. F. Hasler, Apr 20 2015