OFFSET

1,2

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.

LINKS

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

EXAMPLE

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.

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

KEYWORD

base,nonn

AUTHOR

Eric Angelini, Aug 26 2023

EXTENSIONS

Data corrected by Giorgos Kalogeropoulos

STATUS

approved