A380428 Numbers k for which nonnegative integers x and y exist such that k is the concatenation of x and y as well as k = (x + y)^2.

81, 100, 2025, 3025, 88209, 494209, 4941729, 7441984, 24502500, 25502500, 52881984, 60481729, 300814336, 493817284, 6049417284, 6832014336, 20408122449, 21948126201, 33058148761, 35010152100, 43470165025, 101558217124, 108878221089, 123448227904, 127194229449, 152344237969

Offset

1,1

Comments

Subsequence of A000290.

Links

Table of n, a(n) for n=1..26.

Example

2025 is in the sequence because (20 + 25)^2 = 2025.
100 is in the sequence because (10 + 0)^2 = 100.
88209 is in the sequence because (88 + 209)^2 = 88209.

Maple

A380428:=proc(n)
    option remember;
    local a, i, k, x, y;
    if n=1 then
        81
    elif n=2 then
        100
    else
        for a from isqrt(procname(n-1))+1 do
            k:=length(a^2);
            for i to k-1 do
                x:=floor(a^2/10^i);
                y:=a^2-x*10^i;
                if x+y=a and length(x)+length(y)=k then
                    return a^2
                fi
            od
        od
    fi; 	
end proc;
seq(A380428(n), n=1..26);

Crossrefs

Cf. A000290, A115527-A115556.

Sequence in context: A117686 A104113 A102766 * A256349 A202002 A249613

Adjacent sequences: A380425 A380426 A380427 * A380429 A380430 A380431

Keyword

nonn,base,easy

Author

Felix Huber, Jan 25 2025

Status

approved