A078193 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.

1, 34, 789, 3456, 12345, 123456, 3456789, 78901234, 345678901, 1234567890, 12345678901, 345678901234, 7890123456789, 34567890123456, 123456789012345, 1234567890123456, 34567890123456789, 789012345678901234, 3456789012345678901, 12345678901234567890

Offset

1,2

Comments

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

Links

Alois P. Heinz, Table of n, a(n) for n = 1..1000

Maple

a:= n-> parse(cat(map(x-> irem(x, 10), (t-> [$t+1..t+n])(n*(n-1)))[])):
seq(a(n), n=1..20);  # Alois P. Heinz, Feb 13 2021

Mathematica

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 *)

Prog

(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

Crossrefs

Cf. A078194, A078195.

Sequence in context: A028023 A025190 A160315 * A063843 A395711 A368527

Adjacent sequences: A078190 A078191 A078192 * A078194 A078195 A078196

Keyword

base,nonn

Author

Amarnath Murthy, Nov 21 2002

Extensions

More terms from R. J. Mathar, May 19 2006

Status

approved