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A137225 Triangle T(k,q) of minimal q-Niven numbers: smallest number such that the sum of its digits in base q equals k, 2<=q<=k+1.

%I A137225 #2 Mar 30 2012 17:39:31
%S A137225 1,3,2,7,5,3,15,8,7,4,31,17,11,9,5,63,26,15,14,11,6,127,53,31,19,17,
%T A137225 13,7,255,80,47,24,23,20,15,8,511,161,63,49,29,27,23,17,9,1023,242,
%U A137225 127,74,35,34,31,26,19,10,2047,485,191,99,71,41,39,35,29,21,11,4095,728,255
%N A137225 Triangle T(k,q) of minimal q-Niven numbers: smallest number such that the sum of its digits in base q equals k, 2<=q<=k+1.
%H A137225 H. Fredricksen, E. J. Ionascu, F. Luca, P. Stanica, <a href="http://arXiv.org/abs/0803.0477">Minimal Niven numbers</a>, arXiv:0803.0477 [math.NT]
%F A137225 T(k,2)=A000225(k). T(k,k+1)=2k-1. Conjecture: T(k,3)=A062318(k), verified up to k=23.
%e A137225 T(8,4) =47 because 47, written 233 in base q=4, is the smallest number with
%e A137225 digit sum 2+3+3=8=k in base q=4. The triangle reads T(k,q), k=1,2,...,
%e A137225 2<=q up to the diagonal, after which the values stay constant:
%e A137225 1 1 1 1 1 1 1 1 1
%e A137225 3 2 2 2 2 2 2 2 2
%e A137225 7 5 3 3 3 3 3 3 3
%e A137225 15 8 7 4 4 4 4 4 4
%e A137225 31 17 11 9 5 5 5 5 5
%e A137225 63 26 15 14 11 6 6 6 6
%e A137225 127 53 31 19 17 13 7 7 7
%e A137225 255 80 47 24 23 20 15 8 8
%e A137225 511 161 63 49 29 27 23 17 9
%e A137225 1023 242 127 74 35 34 31 26 19
%e A137225 ...
%p A137225 sd := proc(n,b) local i ; add(i,i=convert(n,base,b)) ; end: T := proc(k,q) local a; for a from 1 do if sd(a,q) = k then RETURN(a) ; fi ; od: end: for k from 1 to 20 do for q from 2 to k+1 do printf("%d, ",T(k,q)) ; od: od:
%Y A137225 Cf. A005349, A052491.
%K A137225 base,easy,nonn,tabl
%O A137225 1,2
%A A137225 _R. J. Mathar_, Mar 07 2008