A324550 Primes written in primorial base (A049345).

10, 11, 21, 101, 121, 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, 10001, 10201, 10221, 10301, 10321, 10421, 11001, 11121, 11221

Offset

1,1

Comments

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.

By writing down terms from a(6) to a(46) (primes 13 .. 199):

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,

and then from a(48) to a(80) (primes 223 .. 409):

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,

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.

Links

Antti Karttunen, Table of n, a(n) for n = 1..317

Index entries for sequences related to primorial base.

Formula

a(n) = A049345(A000040(n)).

Mathematica

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 *)

Prog

(PARI) A324550(n) = A049345(prime(n)); \\ For A049345, see under that entry.

Crossrefs

Cf. A000040, A018239, A049345, A324642, A324656, A324657.

Cf. also A004676, A214617, A286941.

Sequence in context: A041475 A041204 A041202 * A214617 A041200 A041847

Adjacent sequences: A324547 A324548 A324549 * A324551 A324552 A324553

Keyword

nonn,base

Author

Antti Karttunen, Mar 11 2019

Status

approved