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A078193
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In the following triangle the n-th row contains n n-digit (or (n-1)-digit) numbers whose concatenation (with a 0 prefixed for (n-1)-digit numbers) gives a substring of the cyclic concatenation of 1,2,3,4,5,6,7,8,9,0,1,2,3,4,5,6,7,8,9,0,1,2,...: 1; 12 34; 123 456 789; 1234 5678 9012 3456; 12345 67890 12345 67890 12345; ... Sequence contains the final terms of rows.
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3
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1, 34, 789, 3456, 12345, 123456, 3456789, 78901234, 345678901, 1234567890, 12345678901, 345678901234, 7890123456789, 34567890123456, 123456789012345, 1234567890123456, 34567890123456789, 789012345678901234, 3456789012345678901, 12345678901234567890
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OFFSET
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1,2
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COMMENTS
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Leading digit is ((n-1)*n+1) mod 10, zero allowed and therefore one more than the least significant digit in A002378(n-1). - R. J. Mathar, May 19 2006
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LINKS
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MAPLE
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a:= n-> parse(cat(map(x-> irem(x, 10), (t-> [$t+1..t+n])(n*(n-1)))[])):
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MATHEMATICA
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Table[FromDigits[Last[Partition[PadRight[{}, n^2, {1, 2, 3, 4, 5, 6, 7, 8, 9, 0}], n]]], {n, 20}] (* Harvey P. Dale, Dec 13 2022 *)
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PROG
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(PARI) A078193(n)= { local(a, f) ; a= (n*(n-1)+1) %10 ; f=a ; for(i=1, n-1, a=Str(Str(a) Str((f+i)%10)) ; a=eval(a) ; ) ; return(a) ; } { for(n=1, 20, print1(A078193(n), ", ") ; ) ; } \\ R. J. Mathar, May 19 2006
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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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