A363758 -id:A363758 - cp's OEIS frontend

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

Kevin Ryde, Sep 28 2022

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.

			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.

Kevin Ryde, Table of n, a(n) for n = 0..472
Kevin Ryde, C Code (revised)
Index entries for sequences related to fractional bases

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

C
```
/* See links. */
```

A364751 Minimum sum of digits for any number of length n digits in fractional base 4/3.

Original entry on oeis.org

0, 3, 5, 6, 6, 8, 8, 9, 10, 10, 11, 11, 11, 11, 13, 14, 16, 17, 17, 17, 18, 19, 21, 22, 22, 23, 24, 26, 26, 26, 27, 28, 29, 29, 29, 29, 29, 29, 31, 33, 34, 35, 36, 37, 38, 38, 38, 39, 39, 41, 41, 42, 42, 43, 43, 45, 45, 46, 46, 48, 50, 50, 52, 52, 52, 52, 53, 55

Offset: 1

Kevin Ryde, Sep 07 2023

0 is taken to be 1 digit long so a(1) = 0.

Terms can be derived from A364779 by a(n) = s for the smallest s where k = A364779(s) is >= n digits long (noting that stripping trailing 0's from k suffices to show numbers with sum of digits s exist at each length down to where sum s-1 exists).

Kevin Ryde, Table of n, a(n) for n = 1..209
Kevin Ryde, Mean Digit Plot
Index entries for sequences related to fractional bases

Cf. A024631 (base 4/3), A244041 (sum of digits), A364779 (largest with sum).

Cf. A363758 (maximum sum).

a(n) = Min_{4*A087192(n-1) <= k < 4*A087192(n)} A244041(k), for n >= 2.

cp's OEIS Frontend

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

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

C