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A365221
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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.
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0
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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
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OFFSET
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1,2
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COMMENTS
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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.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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CROSSREFS
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KEYWORD
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base,nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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