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A341037
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The successive remainders of the division by (a(n) + a(n+1)) of concat(a(n),a(n+1)) rebuild the sequence itself.
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0
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1, 3, 5, 30, 12, 4, 10, 6, 2, 26, 23, 75, 72, 40, 16, 33, 44, 54, 93, 406, 592, 4407, 5591, 44408, 55590, 4398, 5600, 44399, 55599, 94398, 393325, 106674, 8303, 1695, 800, 198, 96, 51, 47, 452, 546, 42, 56, 8, 20, 15, 9, 89, 410, 80, 18, 24, 25, 45, 53, 446
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OFFSET
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1,2
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COMMENTS
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Lexicographically earliest sequence of distinct terms > 0 with this property.
The sequence is conjectured to be a permutation of the integers > 0.
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LINKS
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EXAMPLE
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1 and 3 -> 13/4 with remainder 1
3 and 5 -> 35/8 with remainder 3
5 and 30 -> 530/35 with remainder 5
30 and 12 -> 3012/42 with remainder 30
12 and 4 -> 124/16 with remainder 12
4 and 10 -> 410/14 with remainder 4
10 and 6 -> 106/16 with remainder 10
6 and 2 -> 62/8 with remainder 6; etc.
The first and last column are identical.
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MATHEMATICA
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a[1]=1; a[n_]:=a[n]=Block[{k=1}, While[MemberQ[Array[a, n-1], k]||Mod[FromDigits@Flatten[IntegerDigits/@{a[n-1], k}], a[n-1]+k]!=a[n-1], k++]; k]; Array[a, 27] (* Giorgos Kalogeropoulos, May 11 2022 *)
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PROG
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(PARI) lista(nn) = {my(k, v=vector(nn)); v[1]=1; for(i=1, nn-1, k=1; until(eval(Str(v[i], k))%(v[i]+k)==v[i]&&!vecsearch(vecsort(v), k), k++); v[i+1]=k); v; } \\ Jinyuan Wang, Feb 10 2021
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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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EXTENSIONS
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STATUS
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approved
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