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%I #17 Mar 06 2024 01:01:09
%S 10,11,21,101,121,201,221,301,321,421,1001,1101,1121,1201,1221,1321,
%T 1421,2001,2101,2121,2201,2301,2321,2421,3101,3121,3201,3221,3301,
%U 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 Primes written in primorial base (A049345).
%C 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 By writing down terms from a(6) to a(46) (primes 13 .. 199):
%C 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 and then from a(48) to a(80) (primes 223 .. 409):
%C 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 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 Antti Karttunen, <a href="/A324550/b324550.txt">Table of n, a(n) for n = 1..317</a>
%H <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%F a(n) = A049345(A000040(n)).
%t 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 (PARI) A324550(n) = A049345(prime(n)); \\ For A049345, see under that entry.
%Y Cf. A000040, A018239, A049345, A324642, A324656, A324657.
%Y Cf. also A004676, A214617.
%K nonn,base
%O 1,1
%A _Antti Karttunen_, Mar 11 2019
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