cp's OEIS Frontend

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

%I A376252 #36 Oct 26 2024 10:04:47
%S A376252 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,
%T A376252 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,
%U A376252 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
%N A376252 Concatenated (n+1)||n modulo n.
%C A376252 There is an interesting and striking pattern in the graph of this sequence that appears at n >= 20 and appears to continue indefinitely.
%C A376252 There does not appear to be a corresponding pattern for other bases.
%C A376252 Beyond the first two terms, zeros only appear where n is a multiple of 5.
%F A376252 a(n) = 10^A055642(n) mod n. Concatenation of 1||n modulo n. - _Chai Wah Wu_, Oct 01 2024
%e A376252 For n=2: 32 mod 2 is 0.
%e A376252 For n=123: 124123 mod 123 is 16.
%t A376252 a[n_]:=Mod[FromDigits[Join[IntegerDigits[n+1],IntegerDigits[n]]],n]; Array[a,80] (* _Stefano Spezia_, Sep 18 2024 *)
%o A376252 (PARI) a(n) = eval(concat(Str(n+1), Str(n))) % n; \\ _Michel Marcus_, Sep 17 2024
%o A376252 (PARI) a(n) = 10*10^logint(n, 10) % n; \\ _Ruud H.G. van Tol_, Oct 26 2024
%o A376252 (Python)
%o A376252 def a(n): return int(str(n+1)+str(n))%n
%o A376252 print([a(n) for n in range(1, 81)]) # _Michael S. Branicky_, Sep 17 2024
%o A376252 (Python)
%o A376252 def A376252(n): return int('1'+str(n))%n # _Chai Wah Wu_, Oct 01 2024
%Y A376252 Cf. A055642, A127423.
%K A376252 nonn,base,easy
%O A376252 1,4
%A A376252 _Stuart Coe_, Sep 17 2024