A357425 Smallest number for which the sum of digits in fractional base 4/3 is n.

0, 1, 2, 3, 5, 6, 7, 10, 11, 15, 21, 22, 23, 31, 39, 43, 54, 55, 74, 75, 101, 102, 103, 138, 139, 183, 187, 246, 247, 330, 331, 439, 443, 587, 783, 790, 791, 1047, 1355, 1398, 1399, 1866, 1867, 2487, 2491, 3318, 3319, 4199, 4427, 5903, 5911, 7882, 7883, 9959

Offset

0,3

Comments

The sum of digits is A244041 and k = a(n) is the smallest A244041(k) = n.

Terms are never multiples of 4, after a(0)=0, since a multiple of 4 is a final 0 digit in base 4/3 which can be removed for the same digit sum.

Terms are strictly increasing (and so are indices of record highs in A244041) since a(n) - 1 has sum of digits n-1 and so is an upper bound for a(n-1).

If a(n) != 3 (mod 4), then the next term is a(n+1) = a(n) + 1 by incrementing the least significant digit.

If a(n) == 3 (mod 4), then an upper bound on the next term is a(n+1) <= (a(n) - r)*4/3 + r+1, where r = a(n) mod 3, by reducing the last digit to reach a multiple of 3 then append a suitable additional digit.

Links

Kevin Ryde, Table of n, a(n) for n = 0..472

Kevin Ryde, C Code (revised)

Index entries for sequences related to fractional bases

Example

For n=10, a(10) = 21 = 32131 in base 4/3 is the smallest number with sum of digits = 10.
For n=11, a(11) = 22 = 32132 in base 4/3, and which differs from a(10) simply by increasing the least significant base 4/3 digit.

Prog

(C) /* See links. */

Crossrefs

Cf. A024631 (base 4/3), A244041 (sum of digits), A363758.

Sequence in context: A102830 A031989 A023746 * A090034 A037016 A308981

Adjacent sequences: A357422 A357423 A357424 * A357426 A357427 A357428

Keyword

nonn,base

Author

Kevin Ryde, Sep 28 2022

Status

approved