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%I #13 Dec 13 2022 14:44:10
%S 1,34,789,3456,12345,123456,3456789,78901234,345678901,1234567890,
%T 12345678901,345678901234,7890123456789,34567890123456,
%U 123456789012345,1234567890123456,34567890123456789,789012345678901234,3456789012345678901,12345678901234567890
%N 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.
%C 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
%H Alois P. Heinz, <a href="/A078193/b078193.txt">Table of n, a(n) for n = 1..1000</a>
%p a:= n-> parse(cat(map(x-> irem(x, 10), (t-> [$t+1..t+n])(n*(n-1)))[])):
%p seq(a(n), n=1..20); # _Alois P. Heinz_, Feb 13 2021
%t 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 *)
%o (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
%Y Cf. A078194, A078195.
%K base,nonn
%O 1,2
%A _Amarnath Murthy_, Nov 21 2002
%E More terms from _R. J. Mathar_, May 19 2006
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