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%I #20 Jun 19 2021 13:02:53
%S 2,5,10,17,26,37,50,65,82,2,3,5,10,17,26,37,50,65,82,5,5,9,13,17,26,
%T 37,50,65,82,10,10,13,19,25,31,37,50,65,82,17,17,17,25,33,41,49,57,65,
%U 82,26,26,26,31,41,51,61,71,81,91,37,37,37,37,49,61,73,85,97,109
%N Smallest number b such that the number whose digits are n in base b is a skinny number.
%C I assume that "the number whose digits are n in base b" means the number Sum c_i b^i, where the decimal expansion of n is Sum c_i 10^i. - _N. J. A. Sloane_, Jun 19 2021
%F a(n) <= 10 iff n is in A061909.
%e a(10) = 2 because 10^2 = 100 in all bases >= 2.
%e a(14) = 17 because 14_16 = 20_10, so the square is 400_10 = (1,9,0)_16, but digitsum((1,9,0)_16) = 10 != digitsum((1,4)_16)^2; while in base 17, 14_17 = 21_10, so the square is 441_10 = (1,8,16)_17 and digitsum((1,8,16)_17) = 25 = digitsum((1,4)_17)^2.
%o (PARI) a(n) = my(d=digits(n), s); s=vecsum(d); for(b=1+vecmax(d), oo, if(s^2==sumdigits(fromdigits(d, b)^2, b), return(b))); \\ _Jinyuan Wang_, Jun 19 2021
%Y Cf. A061909.
%K nonn,base
%O 1,1
%A _J. Lowell_, Apr 14 2009
%E More terms from _Jinyuan Wang_, Jun 19 2021
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