A376252 - OEIS

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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

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,4

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.

LINKS

Table of n, a(n) for n=1..80.

FORMULA

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

EXAMPLE

For n=2: 32 mod 2 is 0.

For n=123: 124123 mod 123 is 16.

MATHEMATICA

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

PROG

(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

CROSSREFS

Cf. A055642, A127423.

Sequence in context: A078909 A067458 A088330 * A347323 A324471 A346576

Adjacent sequences: A376249 A376250 A376251 * A376253 A376254 A376255

KEYWORD

nonn,base,easy

AUTHOR

Stuart Coe, Sep 17 2024

STATUS

approved