A376252 Concatenated (n+1)||n modulo n.

0, 0, 1, 2, 0, 4, 3, 2, 1, 0, 1, 4, 9, 2, 10, 4, 15, 10, 5, 0, 16, 12, 8, 4, 0, 22, 19, 16, 13, 10, 7, 4, 1, 32, 30, 28, 26, 24, 22, 20, 18, 16, 14, 12, 10, 8, 6, 4, 2, 0, 49, 48, 47, 46, 45, 44, 43, 42, 41, 40, 39, 38, 37, 36, 35, 34, 33, 32, 31, 30, 29, 28, 27, 26, 25, 24, 23, 22, 21, 20

Offset: 1

Author

Stuart Coe, Sep 17 2024

Keywords

• nonn
• base
• easy

Comments

There is an interesting and striking pattern in the graph of this sequence that appears at n >= 20 and appears to continue indefinitely.

There does not appear to be a corresponding pattern for other bases.

Beyond the first two terms, zeros only appear where n is a multiple of 5.

Examples

			For n=2: 32 mod 2 is 0.
For n=123: 124123 mod 123 is 16.
		

Crossrefs

Cf. A055642, A127423.

Programs

Mathematica

a[n_]:=Mod[FromDigits[Join[IntegerDigits[n+1],IntegerDigits[n]]],n]; Array[a,80] (* Stefano Spezia, Sep 18 2024 *)

PARI

a(n) = eval(concat(Str(n+1), Str(n))) % n; \\ Michel Marcus, Sep 17 2024

PARI

a(n) = 10*10^logint(n, 10) % n; \\ Ruud H.G. van Tol, Oct 26 2024

Python

def a(n): return int(str(n+1)+str(n))%n
print([a(n) for n in range(1, 81)]) # Michael S. Branicky, Sep 17 2024

Python

def A376252(n): return int('1'+str(n))%n # Chai Wah Wu, Oct 01 2024

Formula

a(n) = 10^A055642(n) mod n. Concatenation of 1||n modulo n. - Chai Wah Wu, Oct 01 2024