A373033 - OEIS

%I #24 May 22 2024 12:55:44

%S 5,11,23,113,1301,110111,122320133,13102213110011,

%T 2332222120300201203323,133212320111123130111021311111121323,

%U 12122133133313032110200332320320202022333020121323230212223,1323212003321221211122101013133003222123113122111221033300222032132012202011331212030120003001333

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

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

%H Paolo Xausa, <a href="/A373033/b373033.txt">Table of n, a(n) for n = 0..15</a>

%H Grant Sanderson, <a href="https://www.youtube.com/watch?v=NOCsdhzo6Jg">How They Fool Ya (live) | Math parody of Hallelujah</a>, 3Blue1Brown YouTube video, 2023.

%F From _Jianing Song_, May 22 2024: (Start)

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

%F 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)

%e 5        -->        11        -->        23 ...

%e   base 10 to base 4    base 10 to base 4

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

%Y Cf. A007090, A023378, A065722.

%K nonn,base,easy

%O 0,1

%A _Paolo Xausa_, May 20 2024