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A068165 Smallest square formed from n by inserting zero or more decimal digits. 8
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 (list; graph; refs; listen; history; text; internal format)
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

Table of n, a(n) for n=1..50.

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

CROSSREFS

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

Sequence in context: A039457 A243749 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

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Last modified March 27 02:08 EDT 2017. Contains 284143 sequences.