A357432 a(1) = 1; a(2) = 2; for n > 2, a(n) is the smallest positive number not occurring earlier such that a(n) plus the sum of all previous terms appears in the string concatenation of a(1)..a(n-1).

1, 2, 9, 17, 62, 38, 47, 115, 93, 87, 122, 30, 88, 51, 85, 4, 3, 31, 32, 21, 221, 64, 68, 302, 53, 116, 92, 268, 42, 48, 18, 78, 76, 97, 50, 153, 233, 108, 63, 20, 8, 16, 89, 12, 77, 537, 24, 377, 83, 46, 306, 28, 107, 197, 170, 126, 61, 566, 218, 82, 43, 25, 14, 148, 147, 6, 209, 145, 37, 103

Offset: 1

Author

Scott R. Shannon, Sep 28 2022

Keywords

• nonn
• base

Comments

The sequence is conjectured to be a permutation of the positive integers. In the first 20000 terms the fixed points are 393, 514, 1546, and 7854, although more likely exist.

Examples

			a(4) = 17 as a(1) + a(2) + a(3) + 17 = 1 + 2 + 9 + 17 = 29, and "29" appears in the string concatenation of a(1)..a(3) = "129".
		

Links

• Scott R. Shannon, Image of the first 20000 terms. The green line is a(n) = n.

Crossrefs

Cf. A357433 (base 2), A000027, A007908, A000217, A351753, A337227.