A371904 a(1) = 1; for n > 1, a(n) is the smallest unused positive number such that 2^a(n) contains a(n-1) as a substring.

1, 4, 2, 5, 8, 3, 14, 18, 30, 22, 43, 25, 41, 44, 38, 23, 58, 33, 63, 55, 16, 24, 10, 17, 27, 15, 21, 31, 49, 32, 45, 28, 7, 20, 11, 40, 12, 9, 13, 37, 47, 36, 29, 60, 59, 35, 52, 19, 53, 79, 34, 65, 42, 50, 54, 39, 61, 62, 66, 46, 64, 6, 26, 71, 48, 51, 57, 56, 68, 75, 67, 78, 74, 70, 69, 72

Offset: 1

Author

Scott R. Shannon, Apr 11 2024

Keywords

• nonn
• base

Comments

The sequence is conjectured to be a permutation of the positive integers.

Examples

			a(2) = 4 as 2^4 = 16 which contains a(n-1) = a(1) = '1' as a substring.
a(7) = 14 as 2^14 = 16384 which contains a(n-1) = a(6) = '3' as a substring. Note that 2^5 = 32 also contains '3' as a substring but 5 has already been used.
		

Links

• Scott R. Shannon, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000079, A063565, A371918, A368866.