A373033 a(0) = 5. For n >= 1, a(n) = a(n-1) converted to base 4 and interpreted in base 10.

5, 11, 23, 113, 1301, 110111, 122320133, 13102213110011, 2332222120300201203323, 133212320111123130111021311111121323, 12122133133313032110200332320320202022333020121323230212223, 1323212003321221211122101013133003222123113122111221033300222032132012202011331212030120003001333

Offset: 0

Author

Paolo Xausa, May 20 2024

Keywords

• nonn
• base
• easy

Comments

a(n) is prime for n = 0, 1, 2, 3, 4. What is the next n for which a(n) is prime?

Examples

			5        -->        11        -->        23 ...
  base 10 to base 4    base 10 to base 4
		

Links

• Paolo Xausa, Table of n, a(n) for n = 0..15
• Grant Sanderson, How They Fool Ya (live) | Math parody of Hallelujah, 3Blue1Brown YouTube video, 2023.

Crossrefs

Cf. A007090, A023378, A065722.

Programs

Mathematica

NestList[FromDigits[IntegerDigits[#, 4]] &, 5, 11]

Formula

From Jianing Song, May 22 2024: (Start)

a(n+1) = A007090(a(n)).

As A007090(n+1) = A007090(n) + 1 if n is not congruent to 3 modulo 4, and all terms of A023378 are even, we have a(n) = A023378(n) + 1 by induction. (End)