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A275482
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The sum of the last digit of a(n) and the first digit of a(n+1) is a divisor of a(n) and a(n+1) concatenated.
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1
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1, 2, 4, 5, 10, 11, 12, 15, 18, 20, 8, 19, 25, 14, 22, 17, 28, 9, 24, 36, 40, 13, 16, 38, 39, 27, 30, 3, 6, 60, 26, 37, 56, 34, 48, 75, 42, 35, 21, 32, 46, 53, 41, 45, 29, 54, 78, 52, 44, 31, 23, 67, 43, 47, 74, 88, 33, 66, 55, 50, 64, 79, 65, 76, 7, 70, 62, 51, 84, 100, 68, 80, 71, 58, 99, 90, 72, 59, 94, 105, 82, 101, 102, 96, 103, 92, 95, 49, 81, 69, 87, 104
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OFFSET
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1,2
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COMMENTS
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Start the sequence with a(1)=1 and always extend it with the smallest integer not yet present in the sequence that does not lead to a contradiction.
It is conjectured that this sequence is a permutation of the nonnegative numbers.
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LINKS
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EXAMPLE
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a(1) = 1.
a(2) = 2 because (1+2) is a divisor of 12 (as 12/3 = 4).
The next term can't be "3" as (2+3)=5 and 5 is not a divisor of 23.
The next term is 4 because (2+4) is a divisor of 24 (as 24/6 = 4).
The next term can't be "3" as (4+3)=7 and 7 is not a divisor of 43.
The next term is 5 because (4+5) is a divisor of 45 (as 45/9 = 5).
The next term still can't be "3" as (5+3)=8 and 8 is not a divisor of 53.
The next term can't be "6" as (5+6)=11 and 11 is not a divisor of 56.
The next term can't be "7" as (5+7)=12 and 12 is not a divisor of 57.
The next term can't be "8" as (5+8)=13 and 13 is not a divisor of 58.
The next term can't be "9" as (5+9)=14 and 14 is not a divisor of 59.
The next term is 10 because (5+1) is a divisor of 510 (as 510/6 = 85).
Etc.
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MATHEMATICA
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a[1] = 1; a[2] = 2; a[n_] := a[n] = Catch[With[{arr = Array[a, n - 1]}, Do[If[! MemberQ[arr, k] && Divisible[FromDigits[Join[IntegerDigits[a[n - 1]], IntegerDigits[k]]], IntegerDigits[a[n - 1]][[-1]] + IntegerDigits[k][[1]]], Throw[k]], {k, Infinity}]]]; Array[a, 50] (* JungHwan Min, Jul 29 2016 *)
a = {1}; Do[k = 1; While[Or[MemberQ[a, k], ! Divisible[FromDigits@ Flatten@ #, #[[1, -1]] + #[[-1, 1]]] &@ IntegerDigits@ {a[[n - 1]], k}], k++]; AppendTo[a, k], {n, 2, 120}]; a (* Michael De Vlieger, Jul 31 2016 *)
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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