A357880 a(1) = a(2) = 1; for n > 2, a(n) is the smallest positive number such that a(n) plus the sum of all previous terms appears in the string concatenation of a(1)..a(n-1).

1, 1, 9, 8, 79, 21, 79, 19, 574, 1, 87, 40, 2, 36, 30, 211, 593, 83, 83, 30, 128, 64, 184, 501, 148, 9, 280, 329, 203, 5, 185, 161, 3, 314, 391, 119, 150, 24, 556, 197, 195, 64, 105, 108, 8, 777, 207, 16, 302, 52, 147, 2, 111, 298, 53, 67, 66, 20, 105, 99, 37, 15, 85, 51, 183, 39, 45, 8, 14

Offset: 1

Author

Scott R. Shannon, Oct 18 2022

Keywords

• nonn
• base

Comments

It is conjectured that all numbers eventually appear. In the first 100000 terms the only fixed point is 210; it is likely no more exist.

Examples

			a(6) = 21 as a(1) + ... + a(5) + 21 = 98 + 21 = 119, and "119" appears in the string concatenation of a(1)..a(5) = "119879".
		

Links

• Michael De Vlieger, Table of n, a(n) for n = 1..10000
• Scott R. Shannon, Image of the first 100000 terms. The green line is a(n) = n.

Crossrefs

Cf. A357432, A357433, A000027, A007908, A000217, A351753, A337227.

Programs

Mathematica

nn = 120; a[1] = a[2] = 1; s = 2; w = "11"; Do[k = 1; While[! StringContainsQ[w, ToString[k + s]], k++]; a[n] = k; s += k; w = StringJoin[w, ToString[k]], {n, 3, nn}]; Array[a, nn] (* Michael De Vlieger, Oct 20 2022 *)