A376817 Irregular table read by rows: row(n) lists the positive numbers k in each base n such that the sum of its digits when written in all bases 2 to n equals k, or -1 if no such number exists.

1, 3, 5, 4, 11, 10, 16, 25, 31, 41, -1, 57, 56, 75, 73, 80, -1, 108, 110, 142, 112, 149, 148, 155, 154, 168, 194, 203, 221, 238, -1, 271, -1, -1, 308, -1, 360, 414, 416, 437, -1, -1, 484, -1, -1, 529, -1, 660, -1, 740, 944, 760, 869, 916, 984, -1, 1010, 1016, 1020, -1, 1032, -1, 1193, 1219, 1160, 1329, 1264, 1331, 1200, 1426, 1303, 1350, 1369, 1473, 1543

Offset

2,2

Comments

The first base with two numbers is 3, the first base with three numbers is 14, the first base with four numbers is 88, and the first base with five numbers is 440. It is unknown if a base can contain an arbitrary number of such values.

See A376816 for the smallest number in each base n.

Links

Scott R. Shannon, Table of n, a(n) for n = 2..720

Scott R. Shannon, Unflattened table for n = 2..500

Example

row(4) = 4, 11; as 4 = 100_2 = 11_3 = 10_4, and the sum of all these digits is 1 + 0 + 0 + 1 + 1 + 1 + 0 = 4, and 11 = 1011_2 = 102_3 = 23_4, and the sum of all these digits is 1 + 0 + 1 + 1 + 1 + 0 + 2 + 2 + 3 = 11.
The table begins:
  1;
  3, 5;
  4, 11;
  10;
  16;
  25, 31;
  41;
  -1;
  57;
  56, 75;
  73, 80;
  -1;
  108, 110, 142;
  112, 149;
  148, 155;
  154, 168, 194;
  203;
  221, 238;
  ...

Crossrefs

Cf. A376816, A004209, A007953.

Sequence in context: A078439 A007063 A335500 * A127397 A284048 A326119

Adjacent sequences: A376814 A376815 A376816 * A376818 A376819 A376820

Keyword

sign,base,tabf

Author

Scott R. Shannon, Oct 07 2024

Status

approved