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

1,3

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

Links

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

Example

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.

Mathematica

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

Prog

(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

Crossrefs

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

Sequence in context: A046829 A052212 A046838 * A037359 A099538 A093614

Adjacent sequences: A326415 A326416 A326417 * A326419 A326420 A326421

Keyword

nonn,base

Author

Riccardo Pietro Giovambattista Mazzei and Matteo Albanese, Sep 28 2019

Status

approved