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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.
2
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
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
KEYWORD
base,nonn
AUTHOR
Eric Angelini, Aug 26 2023
EXTENSIONS
Data corrected by Giorgos Kalogeropoulos
STATUS
approved