A052212 -id:A052212 - cp's OEIS frontend

A046834 Internal digits of n^2 include digits of n as subsequence.

50, 60, 250, 500, 600, 760, 1050, 2050, 2500, 3050, 3628, 3710, 3760, 3792, 4050, 4410, 5000, 5010, 5050, 5060, 5250, 6000, 6010, 6050, 6250, 6760, 7050, 7560, 7600, 8050, 8250, 8260, 8882, 9050, 9460, 10050, 10500, 14650, 14651, 20050, 20500

Offset: 1

David W. Wilson

If n is a member then so is 10*n. - Robert Israel, May 07 2020

			a(7) = 1050 is a term because 1050^2 = 1102500; remove the first and last to get internal digits 10250, and 1050 is a subsequence of 10250. - _Robert Israel_, May 07 2020

David A. Corneth, Table of n, a(n) for n = 1..10000 (first 5000 terms from Robert Israel)

Cf. A046831, A052212.

filter:= n -> StringTools:-IsSubSequence(sprintf("%d",n),sprintf("%d",n^2)[2..-2]):
select(filter, [$10..30000]); # Robert Israel, May 07 2020

from itertools import count, islice
def A046834_gen(startvalue=1): # generator of terms >= startvalue
    for k in count(max(startvalue,1)):
        c = iter(str(k**2)[1:-1])
        if all(map(lambda b:any(map(lambda a:a==b,c)),str(k))):
            yield k
A046834_list = list(islice(A046834_gen(),20)) # Chai Wah Wu, Apr 03 2023

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.

Original entry on oeis.org

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

Riccardo Pietro Giovambattista Mazzei and Matteo Albanese, Sep 28 2019

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

			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.

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

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

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

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

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

cp's OEIS Frontend

A046834 Internal digits of n^2 include digits of n as subsequence.

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