A308830 a(n) is the smallest positive integer such that the concatenation, in base 2, of the first n terms is divisible by n.

1, 2, 3, 4, 5, 2, 9, 8, 5, 2, 3, 20, 7, 14, 27, 16, 11, 30, 11, 20, 15, 22, 31, 24, 11, 14, 11, 20, 15, 10, 35, 32, 1, 26, 97, 92, 53, 18, 31, 56, 91, 10, 3, 12, 27, 30, 15, 48, 37, 78, 23, 108, 9, 6, 49, 8, 51, 54, 87, 60, 79, 26, 25, 64, 111, 122, 117, 28

Offset: 1

Author

Rémy Sigrist, Jun 27 2019

Keywords

• nonn
• base

Comments

This sequence is the binary variant of A099552.

Examples

			The first terms, alongside the concatenation of the first n terms, both in decimal and in base 2, are:
  n   a(n)  bin(a(n))  K(n)      bin(K(n))
  --  ----  ---------  --------  --------------------------
   1     1          1         1                           1
   2     2         10         6                         110
   3     3         11        27                       11011
   4     4        100       220                    11011100
   5     5        101      1765                 11011100101
   6     2         10      7062               1101110010110
   7     9       1001    113001           11011100101101001
   8     8       1000   1808024       110111001011010011000
   9     5        101  14464197    110111001011010011000101
  10     2         10  57856790  11011100101101001100010110
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..8192
• Rémy Sigrist, PARI program for A308830

Crossrefs

Cf. A007814, A099552.

Programs

PARI

See Links section.

Formula

a(2^k) = 2^k for any k >= 0.

A007814(a(n)) = A007814(n).