A062318 -id:A062318 - cp's OEIS frontend

A134562 Array T by antidiagonals: T(n,k) = k-th number whose formal base-3 representation has exactly n terms. ("Formal" means that all the nonzero coefficients are 1's.).

1, 3, 2, 9, 4, 5, 27, 6, 7, 8, 81, 10, 11, 14, 17, 243, 12, 13, 16, 23, 26, 729, 18, 15, 20, 25, 44, 53, 2187, 28, 19, 22, 35, 50, 71

Offset: 1

Clark Kimberling, Nov 01 2007

A permutation of the natural numbers. Except for initial terms in some cases, (Row 1) = A000244, (Row 2) = A055235, (Col 1) = A062318. For the analogous base-2 array, see A067576.

			11 = 9 + 1 + 1 is the 3rd largest number (after 5 and 7) that has
a 3-term formal base-3 representation.
Northwest corner:
1 3 9 27 81
2 4 6 10 12
5 7 11 13 15
8 14 16 20 22

Cf. A067576, A000244, A055235, A062318.

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.

Original entry on oeis.org

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

R. J. Mathar, Mar 07 2008

			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
...

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

Cf. A005349, A052491.

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:

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

cp's OEIS Frontend

A134562 Array T by antidiagonals: T(n,k) = k-th number whose formal base-3 representation has exactly n terms. ("Formal" means that all the nonzero coefficients are 1's.).

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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.

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