A365219 -id:A365219 - cp's OEIS frontend

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

Eric Angelini, Aug 26 2023

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.

			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.

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]

Cf. A365217, A365219.

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 *)

Data corrected by Giorgos Kalogeropoulos

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.

Original entry on oeis.org

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

Eric Angelini, Aug 26 2023

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.

			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.

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]

Cf. A365217, A365219, A365220.

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 *)

Data corrected by Giorgos Kalogeropoulos

cp's OEIS Frontend

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.

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