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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. 0
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 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..69.

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

FORMULA

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

EXAMPLE

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

...

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:

CROSSREFS

Cf. A005349, A052491.

Sequence in context: A011384 A128140 A213579 * A213777 A118834 A255547

Adjacent sequences:  A137222 A137223 A137224 * A137226 A137227 A137228

KEYWORD

base,easy,nonn,tabl

AUTHOR

R. J. Mathar, Mar 07 2008

STATUS

approved

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Last modified November 29 04:38 EST 2021. Contains 349416 sequences. (Running on oeis4.)