A377412 - OEIS

%I #10 Oct 30 2024 13:55:41

%S 1,1,1,7,1,1,7,3,1,9,1,31,7,5,3,91,1,1,9,55,1,1,31,3,7,13,5,3,3,9,91,

%T 11,1,33,1,39,9,113,55,7,1,25,1,127,31,121,3,443,7,21,13,87,5,97,3,19,

%U 3,73,9,1199,91,21,11,1387,1,1,33,983,1,1,39,19,9

%N a(n) is the least k > 0 such that k*n belongs to A126684.

%C This sequence is well defined: for any positive integer n, according to the pigeonhole principle, A195156(i) mod n = A195156(j) mod n for some distinct i and j, hence n divides b = abs(A195156(i) - A195156(j)), and as b belongs to A126684, a(n) <= b/n.

%H Rémy Sigrist, <a href="/A377412/b377412.txt">Table of n, a(n) for n = 0..10000</a>

%H Rémy Sigrist, <a href="/A377412/a377412.txt">C++ program</a>

%F a(n) >= A300867(n).

%F a(n) = 1 iff n belongs to A126684.

%e The first terms, alongside the binary expansion of a(n)*n, are:

%e   n   a(n)  bin(a(n)*n)

%e   --  ----  -----------

%e    0     1            0

%e    1     1            1

%e    2     1           10

%e    3     7        10101

%e    4     1          100

%e    5     1          101

%e    6     7       101010

%e    7     3        10101

%e    8     1         1000

%e    9     9      1010001

%e   10     1         1010

%e   11    31    101010101

%e   12     7      1010100

%t (* Increase nmax for n>92 in A377412 *) nmax = 1000; b[n_] := FromDigits[IntegerDigits[n, 2], 4];A126684=Union[A000695 = b /@ Range[0, nmax], 2 A000695][[1 ;; nmax+1]] ;A377412={};Do[k=0;Until[MemberQ[A126684,k*n],k++]; AppendTo[A377412,k],{n,0,72}];A377412 (* _James C. McMahon_, Oct 29 2024 *)

%o (C++) // See Links section.

%Y See A300867 for a similar sequence.

%Y Cf. A032937, A126684, A195156, A377413.

%K nonn,base,easy

%O 0,4

%A _Rémy Sigrist_, Oct 27 2024