A308552 a(n) is the least integer such that concat(a(0), a(1), ..., a(n-1), a(n)) == n-1 (mod n), with a(0) = 0.

0, 0, 1, 1, 1, 4, 1, 1, 1, 7, 9, 10, 11, 6, 5, 4, 3, 16, 17, 24, 19, 23, 7, 5, 9, 9, 35, 4, 19, 15, 29, 12, 31, 2, 17, 24, 31, 23, 7, 42, 39, 10, 23, 42, 51, 24, 37, 38, 39, 14, 9, 34, 51, 15, 15, 59, 59, 5, 27, 37, 59, 27, 13, 56, 15, 44, 49, 0, 59, 43, 69, 23

Offset

0,6

Comments

For any starting value of a(0), a(1)=0 and a(2)=1.

First terms with 1, 2, 3, 4 and 5 digits are a(0)=0, a(11)=10, a(98)=157, a(940)=1739 and a(9044)=18963.

Links

Paolo P. Lava, Table of n, a(n) for n = 0..1000

Example

a(0) = 0 by definition;
a(1) = 0 because 0 mod 1 = 0;
a(2) = 1 because 1 mod 2 = 1;
a(3) = 1 because 11 mod 3 = 2;
a(4) = 1 because 111 mod 4 = 3;
a(5) = 4 because 1114 mod 5 = 4; etc.

Maple

P:=proc(q) local a, b, c, k, n; c:=[]; a:=0;
for k from 1 to 71 do for n from 0 to q do
b:=a*10^length(convert(n, string))+n:
if (b mod k)=k-1 then a:=b; c:=[op(c), n]; break;
fi; od; od; 0, op(c); end: P(10^5);

Crossrefs

Sequence in context: A363977 A073937 A074058 * A368333 A088440 A300253

Adjacent sequences: A308549 A308550 A308551 * A308553 A308554 A308555

Keyword

nonn,base,easy

Author

Paolo P. Lava, Jun 07 2019

Status

approved