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A236181
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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.
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0
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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
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OFFSET
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1,1
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COMMENTS
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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.
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LINKS
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EXAMPLE
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10201 = 101^2 is in the sequence because the central digit 2 equals the sum of the other digits 1+0+0+1.
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MAPLE
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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:
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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