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 A068165 Smallest square formed from n by inserting zero or more decimal digits. 9
 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 Michael De Vlieger, 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 MATHEMATICA Table[If[IntegerQ@ Sqrt@ n, n, k = 1;   Function[a,     Function[t,       While[Function[b,            Function[w,              Nand[Times @@ Boole@ Map[w[[#1]] >= #2 & @@ # &, #] == 1,               Length@SequencePosition[                  Select[b,                   Function[d, MemberQ[#[[All, 1]], d /. 0 -> 10]]],                  a] > 0]]@ RotateLeft@ BinCounts[b, {0, 10, 1}]]@           IntegerDigits[Set[s, k^2]] &@         Apply[Join,          Map[Lookup[t, #] /.             d_ /; IntegerQ@ d :> If[d > 0, {d, #}, {10, #}] &,           Keys@ t]], k++]]@      KeyDrop[PositionIndex@ RotateLeft@ BinCounts[a, {0, 10, 1}], 0]]@    IntegerDigits@ n; s], {n, 50}] (* Michael De Vlieger, May 05 2017, Version 10.1 *) 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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