A357433 -id:A357433 - cp's OEIS frontend

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

Scott R. Shannon, Sep 28 2022

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.

			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".

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

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

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).

Original entry on oeis.org

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

Scott R. Shannon, Oct 18 2022

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.

			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".

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.

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

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 *)

cp's OEIS Frontend

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).

Views

Author

Keywords

Comments

Examples

Links

Crossrefs