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A273363
Numbers m such that the decimal number concat(8,m) is a square.
9
1, 41, 100, 281, 464, 649, 836, 1225, 1796, 2369, 2944, 3521, 4100, 4681, 5264, 5849, 6436, 7025, 7616, 8209, 8804, 9401, 10000, 11801, 13604, 15409, 17216, 19025, 20836, 22649, 24464, 26281, 28100, 29921, 31744, 33569, 35396, 37225
OFFSET
1,2
COMMENTS
Elements are squares of integers in [9, sqrt(90)) * sqrt(10)^k without the leading 8 elements for nonnegative k. - David A. Corneth, May 20 2016
EXAMPLE
41 is a member because 841 = 29^2 is a square.
0 is not a member because 80 is not a square.
MAPLE
t1:=[];
for k from 1 to 50000 do
if issqr(k+8*10^length(k)) then t1:=[op(t1), k]; fi;
od;
t1;
MATHEMATICA
Select[Range[45000], IntegerQ[Sqrt[8 10^IntegerLength[#] + #]] &] (* Vincenzo Librandi, Feb 20 2020 *)
PROG
(PARI) do(n)=my(v=List(), t); for(d=0, n, for(s=sqrtint(81*10^d-1)+1, sqrtint(90*10^d-1), listput(v, s^2-10^d*80))); Vec(v) \\ Charles R Greathouse IV, Nov 26 2016
(Magma) [n: n in [1..20000 ] | IsSquare(Seqint(Intseq(n) cat Intseq(8)))]; // Marius A. Burtea, Mar 21 2019
KEYWORD
nonn,base
AUTHOR
STATUS
approved