A236181 Let x(1)x(2)... x(q) denote the decimal expansion of a number n with q odd. The sequence lists the squares n such that the central digit equals the sum of the other digits.

121, 484, 10201, 10816, 40804, 72900, 1002001, 1008016, 3059001, 4008004, 100020001, 100080016, 151290000, 210250000, 216090000, 234090000, 313290000, 400080004, 10000200001, 10000800016, 10210900401, 11003800201, 11020800400, 14101800001, 30101903001, 30310810000

Offset: 1

Author

Michel Lagneau, Jan 19 2014

Keywords

• nonn
• base

Comments

The numbers that are both perfect squares and palindromes (A033934) are in the sequence. The numbers 104^2, 1004^2, 10004^2,... are in the sequence.

Examples

			10201 = 101^2 is in the sequence because the central digit 2 equals the sum of the other digits 1+0+0+1.
		

Crossrefs

Cf. A000290, A033934.

Programs

Maple

with(numtheory):for n from 2 to 6 do:m:=2*n-2:m1:=floor(sqrt(10^m)):m2:=floor(sqrt(10^(m+1)-1)):for k1 from m1 to m2 do:k:=k1^2:x:=convert(k,base,10):n1:=nops(x):s:=sum('x[j]', 'j'=1..n1):s1:=s-x[n]:if x[n]=s1 then printf(`%d, `,k):else fi:od:od:

Mathematica

cdodQ[n_]:=Module[{id=IntegerDigits[n],len,cd},len=Length[id];cd=If[OddQ[len],id[[(len+1)/2]],9999]; Total[id]-cd==cd]; Select[Range[175000]^2,cdodQ] (* Harvey P. Dale, Aug 04 2024 *)