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A279410
Numbers whose squares have identical middle digits in base 10
1
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, ...
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
KEYWORD
nonn,base
AUTHOR
Olivier Gérard, Dec 12 2016
STATUS
approved