cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

A381935 For any n > 0, a(n) is the least nontrivial multiple of n whose binary expansion has the same number of nonleading zeros as that of n; a(0) = 0.

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%I A381935 #15 Mar 12 2025 17:27:07
%S A381935 0,3,6,15,12,30,30,63,24,45,60,55,60,247,126,255,48,85,90,57,120,189,
%T A381935 110,253,120,175,494,8127,252,1015,510,1023,96,165,170,105,180,185,
%U A381935 114,117,240,205,378,215,220,765,506,14335,240,343,350,765,988,159,16254
%N A381935 For any n > 0, a(n) is the least nontrivial multiple of n whose binary expansion has the same number of nonleading zeros as that of n; a(0) = 0.
%C A381935 This sequence is well defined: for any n > 0: write n as m * 2^k for some odd number m; m divides some Mersenne number M > m (see A352217); M * 2^(k + A023416(m)) is a multiple of n with the desired properties, hence a(n) exists.
%H A381935 Rémy Sigrist, <a href="/A381935/b381935.txt">Table of n, a(n) for n = 0..8192</a>
%H A381935 Rémy Sigrist, <a href="/A381935/a381935.gp.txt">PARI program</a>
%F A381935 a(n) = n * A381934(n).
%e A381935 The first terms, in decimal and in binary, are:
%e A381935   n   a(n)  bin(n)  bin(a(n))
%e A381935   --  ----  ------  ---------
%e A381935    0     0       0          0
%e A381935    1     3       1         11
%e A381935    2     6      10        110
%e A381935    3    15      11       1111
%e A381935    4    12     100       1100
%e A381935    5    30     101      11110
%e A381935    6    30     110      11110
%e A381935    7    63     111     111111
%e A381935    8    24    1000      11000
%e A381935    9    45    1001     101101
%e A381935   10    60    1010     111100
%e A381935   11    55    1011     110111
%e A381935   12    60    1100     111100
%e A381935   13   247    1101   11110111
%e A381935   14   126    1110    1111110
%e A381935   15   255    1111   11111111
%e A381935   16    48   10000     110000
%o A381935 (PARI) \\ See Links section.
%Y A381935 Cf. A023416, A161399, A352217, A381934.
%K A381935 nonn,base
%O A381935 0,2
%A A381935 _Rémy Sigrist_, Mar 10 2025