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.

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, 13, 7, 255, 80, 47, 24, 23, 20, 15, 8, 511, 161, 63, 49, 29, 27, 23, 17, 9, 1023, 242, 127, 74, 35, 34, 31, 26, 19, 10, 2047, 485, 191, 99, 71, 41, 39, 35, 29, 21, 11, 4095, 728, 255

Offset: 1

Author

R. J. Mathar, Mar 07 2008

Keywords

• base
• easy
• nonn
• tabl

Examples

			T(8,4) =47 because 47, written 233 in base q=4, is the smallest number with
digit sum 2+3+3=8=k in base q=4. The triangle reads T(k,q), k=1,2,...,
2<=q up to the diagonal, after which the values stay constant:
1 1 1 1 1 1 1 1 1
3 2 2 2 2 2 2 2 2
7 5 3 3 3 3 3 3 3
15 8 7 4 4 4 4 4 4
31 17 11 9 5 5 5 5 5
63 26 15 14 11 6 6 6 6
127 53 31 19 17 13 7 7 7
255 80 47 24 23 20 15 8 8
511 161 63 49 29 27 23 17 9
1023 242 127 74 35 34 31 26 19
...
		

Links

• H. Fredricksen, E. J. Ionascu, F. Luca, P. Stanica, Minimal Niven numbers, arXiv:0803.0477 [math.NT]

Crossrefs

Cf. A005349, A052491.

Programs

Maple

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:

Formula

T(k,2)=A000225(k). T(k,k+1)=2k-1. Conjecture: T(k,3)=A062318(k), verified up to k=23.