A365219 Each term is a "Go up integer" (GUI), but a(n) + a(n+1) is always a "Go down integer" (GDI). More details in the Comments section.

12, 18, 13, 17, 14, 16, 15, 25, 26, 24, 19, 23, 27, 34, 28, 35, 29, 36, 37, 38, 45, 39, 46, 47, 48, 49, 152, 58, 102, 68, 112, 78, 122, 79, 132, 69, 142, 59, 162, 89, 172, 108, 103, 57, 113, 67, 123, 107, 104, 56, 114, 106, 105, 115, 116, 124, 117, 133, 118, 143, 127, 134, 126, 125, 135, 136, 144, 137, 153, 128

Offset

1,1

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. Accordingly, the R of a GDI is always smaller than its L - the first such integer being 10. 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) = 12.

Links

Table of n, a(n) for n=1..70.

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

Example

a(1) + a(2) = 12 + 18 = 30 and 30 is a GDI;
a(2) + a(3) = 18 + 13 = 31 and 31 is a GDI;
a(3) + a(4) = 13 + 17 = 30 and 30 is a GDI;
a(4) + a(5) = 17 + 14 = 31 and 31 is a GDI;
a(5) + a(6) = 14 + 16 = 30 and 30 is a GDI; etc.

Mathematica

a[1]=12; 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.

Sequence in context: A082241 A077294 A206421 * A232391 A025491 A091196

Adjacent sequences: A365216 A365217 A365218 * A365220 A365221 A365222

Keyword

base,nonn

Author

Eric Angelini, Aug 26 2023

Extensions

Data corrected by Giorgos Kalogeropoulos

Status

approved