A368841 Nonnegative integers whose binary expansions (without leading zeros) have no three equally spaced equal digits.

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, 50, 51, 52, 54, 76, 82, 83, 90, 100, 101, 102, 108, 153, 165, 204

Offset

1,3

Comments

Also numbers k such that A368842(k) = 0.

Also numbers k such that A368857(k) < 3.

This sequence is finite by Van der Waerden's theorem.

Links

Table of n, a(n) for n=1..40.

Wikipedia, Van der Waerden's theorem

Index entries for sequences related to binary expansion of n

Prog

(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); }

Crossrefs

Cf. A005346, A368842, A368857.

Sequence in context: A063037 A286262 A330029 * A201992 A329297 A236562

Adjacent sequences: A368838 A368839 A368840 * A368842 A368843 A368844

Keyword

nonn,base,easy,fini,full

Author

Rémy Sigrist, Jan 07 2024

Status

approved