A365220 Each term is a "Go flat integer" (GFI), but a(n) + a(n+1) is always a "Go up integer" (GUI). More details in the Comments section.

1, 11, 2, 22, 3, 9, 4, 8, 5, 7, 6, 33, 99, 44, 88, 55, 77, 66, 101, 1001, 111, 898, 121, 888, 131, 878, 141, 868, 151, 858, 161, 848, 171, 838, 181, 828, 191, 818, 404, 808, 414, 595, 424, 585, 434, 575, 444, 565, 454, 555, 464, 545, 474, 535, 484, 525, 494, 515, 707, 505, 717, 292, 727, 282, 737, 272, 747, 262

Offset

1,2

Comments

The rightmost digit R of a GUI is always larger than the leftmost digit L of the same GUI. The first such integer is 12, as we need at least two digits for a sound GUI. When R = L we have a "Go flat integer", or GFI. We admit that 0 is the first GFI (followed by 1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 22, 33, 44, 55, 66, 77, 88, 99, 101, 111, 121, etc.) This sequence is the lexicographically earliest of distinct nonnegative terms with this property, starting with a(1) = 1.

Links

Table of n, a(n) for n=1..68.

Eric Angelini, Go down, go up, go flat integers, Personal blog "Cinquante signes", Aug 2023.

Example

a(1) + a(2) = 1 + 11 = 12 and 12 is a GUI;
a(2) + a(3) = 11 + 2 = 13 and 13 is a GUI;
a(3) + a(4) = 2 + 22 = 24 and 24 is a GUI;
a(4) + a(5) = 22 + 3 = 25 and 25 is a GUI;
a(5) + a(6) =  3 + 9 = 12 and 12 is a GUI; etc.

Mathematica

a[1]=1; a[n_]:=a[n]=(k=1; While[Last[i=IntegerDigits@k]!=First@i ||MemberQ[Array[a, n-1], k]||First[i1=IntegerDigits[a[n-1]+k]]>=Last@i1, k++]; k); Array[a, 100] (* Giorgos Kalogeropoulos, Aug 27 2023 *)

Crossrefs

Cf. A365217, A365219.

Sequence in context: A318926 A336874 A040120 * A176592 A336904 A051309

Adjacent sequences: A365217 A365218 A365219 * A365221 A365222 A365223

Keyword

base,nonn

Author

Eric Angelini, Aug 26 2023

Extensions

Data corrected by Giorgos Kalogeropoulos

Status

approved