OFFSET
1,3
COMMENTS
Inspired by A328780.
This sequence is not a duplicate of A052040. The first 72 terms until 96 are exactly the same but a(73) = 104 belongs to this sequence because 104^2 = 10816, but 104 doesn't belong to A052040 because there is one zero digit in the decimal expansion of 104^2.
The nonnegative integers that do not belong to this sequence are divided into three sequences:
1) A104315 = A052040 \ {this sequence}: Numbers k such that k contains at least one zero, but k^2 contains no zero (e.g., 106 with 106^2 = 11236).
2) A134844 = Numbers k such that k contains no zero but k^2 contains at least one zero (e.g., 32 with 32^2 = 1024).
3) A328783 = Numbers k such that k and k^2 contain at least one zero but not the same number of zeros (e.g., 101 with 101^2 = 10201).
LINKS
Giovanni Resta, Table of n, a(n) for n = 1..10000
EXAMPLE
12 and 144 = 12^2 have no digit zero in their decimal representation, so 12 is a term.
203 and 41209 = 203^2 both have one digit zero in their decimal representation, so 203 is also a term.
MAPLE
select(t -> numboccur(0, convert(t^2, base, 10))=numboccur(0, convert(t, base, 10)), [$0..200]); # Robert Israel, Oct 27 2019
MATHEMATICA
Select[Range[0, 105], Equal @@ Total /@ (1 - Sign@ IntegerDigits[{#, #^2}]) &] (* Giovanni Resta, Feb 27 2020 *)
CROSSREFS
KEYWORD
nonn,base
AUTHOR
Bernard Schott, Oct 27 2019
STATUS
approved