|
%I #8 Jan 10 2024 08:01:56
%S 0,1,2,3,4,5,6,9,10,11,12,13,18,19,20,22,25,26,27,36,37,38,41,44,45,
%T 50,51,52,54,76,82,83,90,100,101,102,108,153,165,204
%N Nonnegative integers whose binary expansions (without leading zeros) have no three equally spaced equal digits.
%C Also numbers k such that A368842(k) = 0.
%C Also numbers k such that A368857(k) < 3.
%C This sequence is finite by Van der Waerden's theorem.
%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Van_der_Waerden's_theorem">Van der Waerden's theorem</a>
%H <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%o (PARI) is(n, base = 2) = { my (d = digits(n, base)); for (i = 1, #d-2, forstep (j = i+2, #d, 2, if (d[i]==d[j] && d[i]==d[(i+j)/2], return (0);););); return (1); }
%Y Cf. A005346, A368842, A368857.
%K nonn,base,easy,fini,full
%O 1,3
%A _Rémy Sigrist_, Jan 07 2024
|
