A279410 Numbers whose squares have identical middle digits in base 10

35, 38, 46, 65, 76, 83, 85, 318, 335, 348, 359, 380, 383, 393, 400, 415, 419, 432, 436, 441, 457, 469, 500, 511, 526, 527, 585, 586, 599, 600, 611, 620, 636, 648, 654, 665, 688, 692, 696, 700, 711, 718, 728, 752, 755, 771, 781, 786, 793, 800, 809, 811, 826, 828, 832, 834, 836, 838, 857, 866, 880, 900, 908, 911, 922, 928, 944, 951, 958, 995

Offset

1,1

Comments

The sequence of squares starts: 1225, 1444, 2116, 4225, 5776, 6889, 7225, 101124, 112225, 121104, 128881, 144400, ...

By definition the sequence only contains numbers whose square has an even number of digits in base 10.

The sequence of middle digits starts: 2, 4, 1, 2, 7, 8, 2, 1, 2, 1, 8, 4, 6, 4, 0, ...

Links

Robert Israel, Table of n, a(n) for n = 1..10000

Mail by Lars Blomberg to the Seqfan Mailing list Dec 12 2016

Example

46 is in this sequence because its square, 2116, has its two middle digits equal to 1.

Maple

a:= proc(n) option remember; local k, kk, t;
      for k from 1+`if`(n=1, 0, a(n-1)) do kk:=k^2;
        t:= length(kk);
        if t::even and irem(parse(substring(""||kk,
           t/2..t/2+1)), 11)=0 then return k fi
      od
    end:
seq(a(n), n=1..80);  # Alois P. Heinz, Dec 22 2016

Mathematica

TakeEvenCenter[k_List] :=
If[EvenQ[Length[k]], k[[{Length[k]/2, Length[k]/2 + 1}]], {}]; Module[{rz},
Select[Range[
   1000], (rz = TakeEvenCenter[IntegerDigits[#^2, 10]];
    Length[rz] == 2 && Equal @@ rz) &]]

Crossrefs

Sequence in context: A064610 A030589 A114965 * A061755 A094523 A249429

Adjacent sequences: A279407 A279408 A279409 * A279411 A279412 A279413

Keyword

nonn,base

Author

Olivier Gérard, Dec 12 2016

Status

approved