A338834 -id:A338834 - cp's OEIS frontend

A338835 a(n) is the greatest number not yet in the sequence with the same number of digits and the same sum of digits as n in primorial base.

0, 1, 2, 4, 3, 5, 6, 12, 8, 18, 14, 24, 7, 13, 10, 20, 19, 26, 9, 16, 15, 25, 22, 28, 11, 21, 17, 27, 23, 29, 30, 60, 36, 90, 66, 120, 32, 62, 61, 96, 92, 150, 42, 91, 72, 126, 122, 180, 68, 121, 102, 156, 152, 186, 98, 151, 132, 182, 181, 192, 31, 38, 37, 67

Offset: 0

Rémy Sigrist, Nov 11 2020

This sequence is a self-inverse permutation of the nonnegative integers.

			For n = 8:
- the numbers with 3 digits and sum of digits 2 in primorial base are: 7 ("101"), 8 ("110") and 12 ("200"),
- so a(7) = 12,
     a(8) = 8,
     a(12) = 7.

Rémy Sigrist, Table of n, a(n) for n = 0..2309
Rémy Sigrist, Colored scatterplot of the first 2*3*5*7*11*13 terms (where the color is function of A276150(n))
Rémy Sigrist, PARI program for A338835
Index entries for sequences that are permutations of the natural numbers

Cf. A235224, A276150, A333658, A338829 (decimal analog), A338834 (factorial base analog).

PARI
```
See Links section.
```

A235224(a(n)) = A235224(n).

A276150(a(n)) = A276150(n).

A338829 a(n) is the greatest number not yet in the sequence with the same number of digits and the same sum of digits as n.

Original entry on oeis.org

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 20, 30, 40, 50, 60, 70, 80, 90, 91, 11, 21, 31, 41, 51, 61, 71, 81, 82, 92, 12, 22, 32, 42, 52, 62, 72, 73, 83, 93, 13, 23, 33, 43, 53, 63, 64, 74, 84, 94, 14, 24, 34, 44, 54, 55, 65, 75, 85, 95, 15, 25, 35, 45, 46, 56, 66, 76

Offset: 0

Rémy Sigrist, Nov 11 2020

This sequence is a self-inverse permutation of the nonnegative integers.

We have a fixed point with m digits and sum of digits k whenever A289410(m, k) is odd.

			For n = 23:
- the numbers with 2 digits and sum of digits 5 are: 14, 23, 32, 41 and 50,
- so  a(14) = 50,
      a(23) = 41,
      a(32) = 32,
      a(41) = 23,
      a(50) = 14.

Rémy Sigrist, Table of n, a(n) for n = 0..9999
Rémy Sigrist, Colored scatterplot of the first 10000 terms (where the color is function of the sum of digits of n)
Rémy Sigrist, PARI program for A338829
Index entries for sequences that are permutations of the natural numbers

Cf. A055642, A289410, A331274 (binary analog), A333659, A338834 (factorial base analog), A338835 (primorial base analog).

Block[{a = {}, f, k}, f[x_] := Total@ IntegerDigits@ x; Do[k = f[i]; AppendTo[a, SelectFirst[Range[10^# - 1, 10^(# - 1), -1] &@ Floor[1 + Log10[i]], And[f[#] == k, FreeQ[a, #]] &]], {i, 67}]; a] (* Michael De Vlieger, Nov 13 2020 *)

PARI
```
See Links section.
```

A055642(a(n)) = A055642(n).

A007953(a(n)) = A007953(n).

cp's OEIS Frontend

A338835 a(n) is the greatest number not yet in the sequence with the same number of digits and the same sum of digits as n in primorial base.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

PARI

Formula