cp's OEIS Frontend

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

%I A319021 #21 Jun 27 2023 14:11:31
%S A319021 3,4,9,6,7,10,11,14,27,12,13,18,15,16,19,20,23,28,21,22,29,24,25,32,
%T A319021 35,44,81,30,31,36,33,34,37,38,41,54,39,40,45,42,43,46,47,50,55,48,49,
%U A319021 56,51,52,59,62,71,82,57,58,63,60,61,64,65,68,83,66,67,72
%N A319021 Next larger integer with same sum of digits in base 3 as n.
%C A319021 This sequence is the base-3 variant of A057168 (base-2) and of A228915 (base-10).
%C A319021 All integers except those in A062318 appear in this sequence.
%H A319021 Rémy Sigrist, <a href="/A319021/b319021.txt">Table of n, a(n) for n = 1..10000</a>
%F A319021 a(3^k) = 3^(k+1) for any k >= 0.
%F A319021 A053735(a(n)) = A053735(n).
%e A319021 The first terms, alongside the ternary representations of n and of a(n), are:
%e A319021   n   a(n)  ter(n)  ter(a(n))
%e A319021   --  ----  ------  ---------
%e A319021    1     3      1     10
%e A319021    2     4      2     11
%e A319021    3     9     10    100
%e A319021    4     6     11     20
%e A319021    5     7     12     21
%e A319021    6    10     20    101
%e A319021    7    11     21    102
%e A319021    8    14     22    112
%e A319021    9    27    100   1000
%e A319021   10    12    101    110
%e A319021   11    13    102    111
%e A319021   12    18    110    200
%e A319021   13    15    111    120
%e A319021   14    16    112    121
%e A319021   15    19    120    201
%t A319021 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 *)
%o A319021 (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))
%o A319021 (Python)
%o A319021 def a(n, base=3):
%o A319021     c, b, w = 0, base, 0
%o A319021     while True:
%o A319021         d = n%b
%o A319021         if d+1 < b and c:
%o A319021             return (n+1)*b**w + ((c-1)%(b-1)+1)*b**((c-1)//(b-1))-1
%o A319021         c += d; n //= b; w += 1
%o A319021 print([a(n) for n in range(1, 67)]) # _Michael S. Branicky_, Jul 10 2022 after _Rémy Sigrist_
%Y A319021 Cf. A053735, A057168, A062318, A228915.
%K A319021 nonn,base
%O A319021 1,1
%A A319021 _Rémy Sigrist_, Sep 08 2018