A339449 Numbers k such that there are equal numbers of 0's and 2's and equal numbers of 1's and 3's among the first k digits of the quaternary representation of Pi.

0, 4, 386, 398, 2919434, 2919644, 2919648

Offset: 1

Author

Pontus von Brömssen, Dec 05 2020

Keywords

• nonn
• base
• more

Comments

The terms can also be interpreted as numbers k such that a walk on the square lattice governed by the quaternary digits of Pi is at the origin after k steps, where digit 0 corresponds to a step to the right, 1 to up, 2 to left, and 3 to down.

There are no more terms below 2*10^9.

There are two variations of this sequence, according to the directions each digit corresponds to. In A339450, 0=right, 1=left, 2=up, 3=down. For the case 0=right, 1=up, 2=down, 3=left, the only terms below 2*10^9 are 0, 2, 4, 8.

Examples

			4 is a term because the first four quaternary digits of Pi are 3, 0, 2, 1, one of each digit.
386 is a term because among the first 386 digits there are 99 0's and 99 2's, and 94 1's and 94 3's.
		

Crossrefs

Cf. A004603, A039624, A339450.