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

Author

Eric Angelini, Aug 26 2023

Keywords

• base
• nonn

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.

Examples

			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.
		

Links

• Eric Angelini, Go down, go up, go flat integers, Personal blog "Cinquante signes", Aug 2023.
• Eric Angelini, Go down, go up, go flat integers, Personal blog "Cinquante signes", Aug 2023. [Cached copy]

Crossrefs

Cf. A365217.

Programs

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 *)

Extensions

Data corrected by Giorgos Kalogeropoulos