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.

A342700 For any number n with binary expansion (b(1), b(2), ..., b(k)), the binary expansion of a(n) is (1-floor((b(k)+b(1)+b(2))/2), 1-floor((b(1)+b(2)+b(3))/2), ..., 1-floor((b(k-1)+b(k)+b(1))/2)).

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%I A342700 #12 Jan 10 2024 16:32:32
%S A342700 0,0,2,0,7,0,0,0,15,6,10,0,3,0,0,0,31,14,30,12,23,4,16,0,7,6,2,0,3,0,
%T A342700 0,0,63,30,62,28,63,28,56,24,47,14,42,8,35,0,32,0,15,14,14,12,7,4,0,0,
%U A342700 7,6,2,0,3,0,0,0,127,62,126,60,127,60,120,56,127,62
%N A342700 For any number n with binary expansion (b(1), b(2), ..., b(k)), the binary expansion of a(n) is (1-floor((b(k)+b(1)+b(2))/2), 1-floor((b(1)+b(2)+b(3))/2), ..., 1-floor((b(k-1)+b(k)+b(1))/2)).
%C A342700 This sequence is a variant of A342698; here the value of the k-th bit of a(n) is the less frequent value in the bit triple centered around the k-th bit of n.
%H A342700 Rémy Sigrist, <a href="/A342700/b342700.txt">Table of n, a(n) for n = 0..8191</a>
%H A342700 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A342700 a(n) + A342698(n) = A003817(n).
%F A342700 a(n) = n iff n belongs to A020988.
%e A342700 The first terms, in decimal and in binary, are:
%e A342700   n   a(n)  bin(n)  bin(a(n))
%e A342700   --  ----  ------  ---------
%e A342700    0     0       0          0
%e A342700    1     0       1          0
%e A342700    2     2      10         10
%e A342700    3     0      11          0
%e A342700    4     7     100        111
%e A342700    5     0     101          0
%e A342700    6     0     110          0
%e A342700    7     0     111          0
%e A342700    8    15    1000       1111
%e A342700    9     6    1001        110
%e A342700   10    10    1010       1010
%e A342700   11     0    1011          0
%e A342700   12     3    1100         11
%e A342700   13     0    1101          0
%e A342700   14     0    1110          0
%e A342700   15     0    1111          0
%o A342700 (PARI) a(n) = my (w=#binary(n)); sum(k=0, w-1, ((bittest(n, (k-1)%w)+bittest(n, k%w)+bittest(n, (k+1)%w))<=1) * 2^k)
%Y A342700 Cf. A003817, A020988 (fixed points), A342698.
%K A342700 nonn,base
%O A342700 0,3
%A A342700 _Rémy Sigrist_, Mar 18 2021