A365221 Each term is a "Go flat integer" (GFI), but a(n) + a(n+1) is always a "Go down integer" (GDI). More details in the Comments section.

1, 9, 11, 99, 101, 909, 2, 8, 22, 88, 3, 7, 33, 77, 4, 6, 44, 66, 5, 55, 505, 515, 191, 111, 292, 121, 181, 131, 171, 141, 161, 151, 252, 262, 242, 272, 232, 282, 222, 383, 323, 393, 212, 494, 313, 595, 333, 373, 343, 363, 353, 454, 464, 444, 474, 434, 484, 424, 606, 404, 616, 414, 626, 4004, 636, 4014, 646, 4024

Offset: 1

Author

Eric Angelini, Aug 26 2023

Keywords

• base
• nonn

Comments

The rightmost digit R of a GDI is always smaller than the leftmost digit L of the same GDI. The first such integer is 10, as we need at least two digits for a sound GDI. 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.

Examples

			a(1) + a(2) = 1 + 9 = 10 and 10 is a GDI; a(2) + a(3) = 9 + 11 = 20 and 20 is a GDI;a(3) + a(4) = 11 + 99 = 110 and 110 is a GDI;a(4) + a(5) = 99 + 101 = 200 and 200 is a GDI;a(5) + a(6) = 101 + 909 = 1010 and 1010 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, A365219, A365220.

Programs

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 *)

Extensions

Data corrected by Giorgos Kalogeropoulos