This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
%I A324550 #20 Oct 30 2024 20:47:16
%S A324550 10,11,21,101,121,201,221,301,321,421,1001,1101,1121,1201,1221,1321,
%T A324550 1421,2001,2101,2121,2201,2301,2321,2421,3101,3121,3201,3221,3301,
%U A324550 3321,4101,4121,4221,4301,4421,5001,5101,5201,5221,5321,5421,6001,6121,6201,6221,6301,10001,10201,10221,10301,10321,10421,11001,11121,11221
%N A324550 Primes written in primorial base (A049345).
%C A324550 When the primorial base representation is expressed with decimal digits as here, the sequence stays unambiguous only up to the 317th prime, 2099, written as 96421, because after that primorial base digits larger than 9 would be needed.
%C A324550 By writing down terms from a(6) to a(46) (primes 13 .. 199):
%C A324550 201, 221, 301, 321, 421, 1001, 1101, 1121, 1201, 1221, 1321, 1421, 2001, 2101, 2121, 2201, 2301, 2321, 2421, 3101, 3121, 3201, 3221, 3301, 3321, 4101, 4121, 4221, 4301, 4421, 5001, 5101, 5201, 5221, 5321, 5421, 6001, 6121, 6201, 6221, 6301,
%C A324550 and then from a(48) to a(80) (primes 223 .. 409):
%C A324550 10201, 10221, 10301, 10321, 10421, 11001, 11121, 11221, 11321, 11421, 12001, 12101, 12121, 12201, 12321, 13101, 13121, 13201, 13221, 14001, 14101, 14221, 14301, 14321, 14421, 15101, 15201, 15301, 15321, 15421, 16101, 16121, 16301,
%C A324550 it is clearly seen that if n is a prime, then p+n is also likely to be prime, where p is the next higher primorial (A002110) > n. See also A324656.
%H A324550 Antti Karttunen, <a href="/A324550/b324550.txt">Table of n, a(n) for n = 1..317</a>
%H A324550 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%F A324550 a(n) = A049345(A000040(n)).
%t A324550 a[n_] := Module[{k = Prime[n], p = 2, s = {}, r}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, AppendTo[s, r]; p = NextPrime[p]]; FromDigits[Reverse[s]]]; Array[a, 100] (* _Amiram Eldar_, Mar 06 2024 *)
%o A324550 (PARI) A324550(n) = A049345(prime(n)); \\ For A049345, see under that entry.
%Y A324550 Cf. A000040, A018239, A049345, A324642, A324656, A324657.
%Y A324550 Cf. also A004676, A214617, A286941.
%K A324550 nonn,base
%O A324550 1,1
%A A324550 _Antti Karttunen_, Mar 11 2019