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A365217
Each term is a "Go down integer" (GDI), but a(n) + a(n+1) is always a "Go up integer" (GUI). More details in the Comments section.
3
10, 92, 20, 82, 21, 81, 31, 71, 32, 70, 42, 60, 43, 61, 41, 62, 40, 63, 50, 52, 51, 53, 54, 64, 65, 72, 30, 73, 74, 75, 80, 76, 83, 84, 85, 87, 86, 90, 93, 91, 94, 95, 97, 96, 98, 100, 902, 110, 892, 120, 882, 130, 872, 140, 862, 150, 852, 160, 842, 170, 832, 180, 822
OFFSET
1,1
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. Accordingly, the R of a GUI is always larger than its L - the first such integer being 12. 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) = 10.
LINKS
Eric Angelini, Go down, go up, go flat integers, Personal blog "Cinquante signes", Aug 2023.
EXAMPLE
a(1) + a(2) = 10 + 92 = 102 (a GUI);
a(2) + a(3) = 92 + 20 = 112 (a GUI);
a(3) + a(4) = 20 + 82 = 102 (a GUI);
a(4) + a(5) = 82 + 21 = 103 (a GUI);
a(5) + a(6) = 21 + 81 = 102 (a GUI); etc.
MATHEMATICA
a[1]=10; a[n_]:=a[n]=(k=10; 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. A336611.
Sequence in context: A354380 A015467 A144783 * A227512 A227513 A052266
KEYWORD
base,nonn
AUTHOR
Eric Angelini, Aug 26 2023
STATUS
approved