A376816 - OEIS

A376816

The smallest positive number k 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, 4, 10, 16, 25, 41, -1, 57, 56, 73, -1, 108, 112, 148, 154, 203, 221, -1, 271, -1, -1, 308, -1, 360, 416, -1, -1, 484, -1, -1, 529, -1, 660, -1, 740, 944, 760, 984, -1, 1010, -1, 1032, -1, 1193, 1160, 1264, 1200, 1303, 1369, 1543, 1618, 1560, 1634, 1782, 1773, 1876, 1976, 2002, 2151, 2028, -1, 2327, 2463, -1, 2408, 2615, 2751, 2715, -1, -1, 2810

(list; graph; refs; listen; history; text; internal format)

OFFSET

2,2

COMMENTS

See A376817 for the list all of numbers in each base n.

The sequence is dedicated to Eric Angelini (1951 - 2024).

LINKS

Scott R. Shannon, Table of n, a(n) for n = 2..500

EXAMPLE

a(4) = 4 as 4 = 100_2 = 11_3 = 10_4, and the sum of all these digits is 1 + 0 + 0 + 1 + 1 + 1 + 0 = 4.

a(10) = 57 as 57 = 111001_2 = 2010_3 = 321_4 = 212_5 = 133_6 = 111_7 = 71_8 = 63_9 = 57_10, and the sum of all these digits is 1 + 1 + 1 + 0 + 0 + 1 + 2 + 0 + 1 + 0 + 3 + 2 + 1 + 2 + 1 + 2 + 1 + 3 + 3 + 1 + 1 + 1 + 7 + 1 + 6 + 3 + 5 + 7 = 57.

CROSSREFS

Cf. A376817, A004209, A007953.

Sequence in context: A037952 A281903 A093512 * A081160 A051437 A224073

Adjacent sequences: A376813 A376814 A376815 * A376817 A376818 A376819

KEYWORD

sign,base

AUTHOR

Scott R. Shannon, Oct 05 2024

STATUS

approved