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

Author

Rémy Sigrist, Jan 07 2024

Keywords

• nonn
• base
• easy
• fini
• full

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

• Wikipedia, Van der Waerden's theorem
• Index entries for sequences related to binary expansion of n

Crossrefs

Cf. A005346, A368842, A368857.

Programs

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); }