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

1,1

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.

Links

Table of n, a(n) for n=1..26.

Example

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

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 *)

Crossrefs

Cf. A000290, A033934.

Sequence in context: A062555 A017390 A110722 * A077432 A017654 A183448

Adjacent sequences: A236178 A236179 A236180 * A236182 A236183 A236184

Keyword

nonn,base

Author

Michel Lagneau, Jan 19 2014

Status

approved