OFFSET
1,2
COMMENTS
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
LINKS
Les Reid, Problem #12, Challenge Problem Archive, Missouri State University Math Department, Academic year 2013-2014.
PROG
(PARI) a(n)=for(k=1, 9e9, sumdigits(k^2)==n*sumdigits(k)&&return(k))
CROSSREFS
KEYWORD
nonn,base,more
AUTHOR
M. F. Hasler, Apr 14 2017
EXTENSIONS
a(10)-a(11) from Giovanni Resta, Apr 15 2017
STATUS
approved