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.

A306441 Next larger integer with same number of runs of 1's in its binary representation as n.

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%I A306441 #8 Feb 25 2019 08:25:22
%S A306441 2,3,4,6,9,7,8,12,10,11,13,14,17,15,16,24,18,19,20,22,37,23,25,28,26,
%T A306441 27,29,30,33,31,32,48,34,35,36,38,41,39,40,44,42,43,45,46,53,47,49,56,
%U A306441 50,51,52,54,69,55,57,60,58,59,61,62,65,63,64,96,66,67,68
%N A306441 Next larger integer with same number of runs of 1's in its binary representation as n.
%C A306441 Number of runs of 1's in binary representation is given by A069010.
%C A306441 Each nonnegative number either appears in this sequence or in A002450.
%F A306441 a(A023758(n)) = A023758(n+1) for any n > 1.
%F A306441 a(A043682(n)) = A043682(n+1) for any n > 0.
%F A306441 a(A043683(n)) = A043683(n+1) for any n > 0.
%F A306441 a(A043684(n)) = A043684(n+1) for any n > 0.
%F A306441 a(A043685(n)) = A043685(n+1) for any n > 0.
%F A306441 a(A043686(n)) = A043686(n+1) for any n > 0.
%e A306441 The first terms, in decimal and in binary, are:
%e A306441   n   a(n)  bin(n)  bin(a(n))
%e A306441   --  ----  ------  ---------
%e A306441    1     2       1         10
%e A306441    2     3      10         11
%e A306441    3     4      11        100
%e A306441    4     6     100        110
%e A306441    5     9     101       1001
%e A306441    6     7     110        111
%e A306441    7     8     111       1000
%e A306441    8    12    1000       1100
%e A306441    9    10    1001       1010
%e A306441   10    11    1010       1011
%e A306441   11    13    1011       1101
%e A306441   12    14    1100       1110
%e A306441   13    17    1101      10001
%e A306441   14    15    1110       1111
%e A306441   15    16    1111      10000
%e A306441   16    24   10000      11000
%o A306441 (PARI) r1(n) = my (c=0); while (n, my (v=valuation(n+(n%2),2)); if (n%2, c++); n\=2^v); c
%o A306441 a(n) = my (r=r1(n)); for (k=n+1, oo, if (r==r1(k), return (k)))
%Y A306441 Cf. A002450, A023758, A043682, A043683, A043684, A043685, A043686, A057168, A069010.
%K A306441 nonn,base
%O A306441 1,1
%A A306441 _Rémy Sigrist_, Feb 15 2019