A380714 a(n) = n*(n-1) mod (10^m-1) where m is the number of decimal digits in n.

0, 2, 6, 3, 2, 3, 6, 2, 0, 90, 11, 33, 57, 83, 12, 42, 74, 9, 45, 83, 24, 66, 11, 57, 6, 56, 9, 63, 20, 78, 39, 2, 66, 33, 2, 72, 45, 20, 96, 75, 56, 39, 24, 11, 0, 90, 83, 78, 75, 74, 75, 78, 83, 90, 0, 11, 24, 39, 56, 75, 96, 20, 45, 72, 2, 33, 66

Offset: 1

Author

Giorgos Kalogeropoulos, Mar 27 2025

Keywords

• nonn
• base
• look

Comments

a(n) = 0 if and only if n is a Kaprekar number (A053816).

Links

• Giorgos Kalogeropoulos, Table of n, a(n) for n = 1..9999

Crossrefs

Cf. A002283, A002378, A053816, A055642.

Programs

Maple

a:= n-> n*(n-1) mod (10^length(n)-1):
seq(a(n), n=1..67);  # Alois P. Heinz, Mar 27 2025

Mathematica

Table[Mod[n(n-1), 10^IntegerLength@n - 1], {n,67}]

Python

def a(n): return n*(n-1)%(10**len(str(n))-1)
print([a(n) for n in range(1, 68)]) # Michael S. Branicky, Mar 27 2025

Formula

a(n) = A002378(n-1) mod A002283(A055642(n)).