A068165 Smallest square formed from n by inserting zero or more decimal digits.

1, 25, 36, 4, 25, 16, 576, 81, 9, 100, 121, 121, 1369, 144, 1156, 16, 1764, 1089, 169, 2025, 121, 225, 2304, 324, 25, 256, 2704, 289, 289, 2304, 361, 324, 3136, 324, 3025, 36, 3721, 3481, 1369, 400, 441, 4225, 4356, 144, 4225, 4096, 4761, 484, 49, 2500

Offset

1,2

Comments

The digits may be added before, in the middle of, or after the digits of n.

If n is a square then a(n) = n. - Zak Seidov, Nov 13 2014

Links

Michael S. Branicky, Table of n, a(n) for n = 1..10000

Example

Smallest square formed from 20 is 2025, by placing 25 on the right side. Smallest square formed from 33 is 3136, by inserting a 1 between 3's and placing a 6.

Maple

A068165 := proc(n)
        local b, pdigs, plen, dmas, dmasdigs, i, j;
        for b from 1 do
                pdigs := convert(b^2, base, 10) ;
                plen := nops(pdigs) ;
                for dmas from 2^plen-1 to 0 by -1 do
                        dmasdigs := convert(dmas, base, 2) ;
                        pdel := [] ;
                        for i from 1 to nops(dmasdigs) do
                                if op(i, dmasdigs) = 1 then
                                        pdel := [op(pdel), op(i, pdigs)] ;
                                end if;
                        end do:
                        if n = add(op(j, pdel)*10^(j-1), j=1..nops(pdel)) then
                                return b^2;
                        end if;
                end do:
        end do:
end proc:
seq(A068165(n), n=1..133) ; # R. J. Mathar, Nov 14 2014

Prog

(Python)
from math import isqrt
from itertools import count
def dmo(n, t):
    if t < n: return False
    while n and t:
        if n%10 == t%10:
            n //= 10
        t //= 10
    return n == 0
def a(n):
    return next(t for t in (i*i for i in count(isqrt(n))) if dmo(n, t))
print([a(n) for n in range(1, 77)]) # Michael S. Branicky, Jan 21 2023

Crossrefs

A091873 gives square roots. Cf. A038690, A029944, A068164.

Sequence in context: A243749 A331143 A031366 * A086935 A077689 A018796

Adjacent sequences: A068162 A068163 A068164 * A068166 A068167 A068168

Keyword

base,easy,nonn

Author

Amarnath Murthy, Feb 25 2002

Extensions

Corrected and extended by Ray Chandler, Oct 11 2003

Status

approved