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A280012
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a(n) = least positive integer k such that sumdigits(k^2) = n*sumdigits(k).
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5
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1, 2, 3, 13, 113, 1113, 11113, 211113, 101011113, 1101111211, 110101111211
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OFFSET
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1,2
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COMMENTS
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a(n) exists for any n, since sum_{i=0..n-1} 10^(2^i-1) is an integer with the required property, having n digits 1, with its square having n digits 1 at positions 2^i-1 (n>=i>=1), and n(n-1)/2 digits 2 at positions 2^i+2^j-1 (n>=i>j>=0 i.e. at positions 1<=k<2^(n+1) for k in A099628).
a(12) <= 21201101101122, a(13) <= 10101010101101122. - Giovanni Resta, Apr 15 2017
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LINKS
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Les Reid, Problem #12, Challenge Problem Archive, Missouri State University Math Department, Academic year 2013-2014.
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PROG
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(PARI) a(n)=for(k=1, 9e9, sumdigits(k^2)==n*sumdigits(k)&&return(k))
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CROSSREFS
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KEYWORD
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nonn,base,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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