A326418 Nonnegative numbers k such that, in decimal representation, the subsequence of digits of k^2 occupying an odd position is equal to the digits of k.

0, 1, 5, 6, 10, 11, 50, 60, 76, 100, 105, 110, 500, 501, 505, 506, 600, 605, 756, 760, 826, 1000, 1001, 1050, 1100, 5000, 5010, 5050, 5060, 5941, 6000, 6050, 7560, 7600, 8260, 10000, 10005, 10010, 10500, 10505, 11000, 12731

Offset: 1

Author

Riccardo Pietro Giovambattista Mazzei and Matteo Albanese, Sep 28 2019

Keywords

• nonn
• base

Comments

If k is in the sequence then so is 10*k. - David A. Corneth, Sep 29 2019

No term starts with the digit 2. - Chai Wah Wu, Apr 04 2023

Examples

			5^2 = 25, whose first digit is 5, hence 5 is a term of the sequence.
11^2 = 121, whose first and third digit are (1, 1), hence 11 is a term of the sequence.
756^2 = 571536, whose digits in odd positions - starting from the least significant one - are (7, 5, 6), hence 756 is a term of the sequence.
		

Links

• David A. Corneth, Table of n, a(n) for n = 1..2361 (terms < 10^15; first 485 terms from Charles R Greathouse IV)

Crossrefs

Subsequence of A008851, A029772, A046829, A064827, A052212, A189056.

Programs

Mathematica

Select[Range[0, 13000], Reverse@ #[[-Range[1, Length@ #, 2]]] &@ IntegerDigits[#^2] === IntegerDigits[#] &] (* Michael De Vlieger, Oct 06 2019 *)

PARI

isok(n) = my(d=Vecrev(digits(n^2))); fromdigits(Vecrev(vector((#d+1)\2, k, d[2*k-1]))) == n; \\ Michel Marcus, Oct 01 2019

Python

def ok(n): s = str(n*n); return n == int("".join(s[1-len(s)%2::2]))
print(list(filter(ok, range(13000)))) # Michael S. Branicky, Sep 10 2021