A319021 Next larger integer with same sum of digits in base 3 as n.

3, 4, 9, 6, 7, 10, 11, 14, 27, 12, 13, 18, 15, 16, 19, 20, 23, 28, 21, 22, 29, 24, 25, 32, 35, 44, 81, 30, 31, 36, 33, 34, 37, 38, 41, 54, 39, 40, 45, 42, 43, 46, 47, 50, 55, 48, 49, 56, 51, 52, 59, 62, 71, 82, 57, 58, 63, 60, 61, 64, 65, 68, 83, 66, 67, 72

Offset: 1

Author

Rémy Sigrist, Sep 08 2018

Keywords

• nonn
• base

Comments

This sequence is the base-3 variant of A057168 (base-2) and of A228915 (base-10).

All integers except those in A062318 appear in this sequence.

Examples

			The first terms, alongside the ternary representations of n and of a(n), are:
  n   a(n)  ter(n)  ter(a(n))
  --  ----  ------  ---------
   1     3      1     10
   2     4      2     11
   3     9     10    100
   4     6     11     20
   5     7     12     21
   6    10     20    101
   7    11     21    102
   8    14     22    112
   9    27    100   1000
  10    12    101    110
  11    13    102    111
  12    18    110    200
  13    15    111    120
  14    16    112    121
  15    19    120    201
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A053735, A057168, A062318, A228915.

Programs

Mathematica

nli3[n_]:=Module[{nd3=Total[IntegerDigits[n,3]],k=n+1},While[Total[IntegerDigits[k,3]]!=nd3,k++];k]; Array[nli3,70] (* Harvey P. Dale, Jun 27 2023 *)

PARI

a(n, base=3) = my (c=0); for (w=0, oo, my (d=n % base); if (d+1 < base && c, return ((n+1)*base^w + ((c-1)%(base-1) + 1)*base^((c-1)\(base-1))-1), c += d; n \= base))

Python

def a(n, base=3):
    c, b, w = 0, base, 0
    while True:
        d = n%b
        if d+1 < b and c:
            return (n+1)*b**w + ((c-1)%(b-1)+1)*b**((c-1)//(b-1))-1
        c += d; n //= b; w += 1
print([a(n) for n in range(1, 67)]) # Michael S. Branicky, Jul 10 2022 after Rémy Sigrist

Formula

a(3^k) = 3^(k+1) for any k >= 0.

A053735(a(n)) = A053735(n).