A370132 Numbers with no digit larger than 2 in primorial base, A049345.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 210, 211, 212, 213, 214, 215, 216, 217, 218, 219, 220, 221, 222, 223, 224, 225, 226, 227, 240, 241, 242, 243

Offset: 1

Author

Antti Karttunen, Feb 10 2024

Keywords

• nonn
• base

Comments

Numbers k for which A328114(k) <= 2.

Numbers k such that A276086(k) is cubefree (in A004709).

Links

• Antti Karttunen, Table of n, a(n) for n = 1..13122
• Index entries for sequences related to primorial base.

Crossrefs

Cf. A004709, A049345, A276086, A328114.

Subsequence of A370133.

Subsequences: A328242, A276156 and its subsequences: A002110, A143293.

Programs

Mathematica

q[n_] := Module[{k = n, p = 2, s = {}, r}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, AppendTo[s, r]; p = NextPrime[p]]; Count[s, ?(# > 2 &)] == 0]; Select[Range[0, 250], q] (* _Amiram Eldar, Mar 06 2024 *)

PARI

ismaxprimobasedigit_at_most(n,k) = { my(s=0, p=2); while(n, if((n%p)>k, return(0)); n = n\p; p = nextprime(1+p)); (1); };
isA370132(n) = ismaxprimobasedigit_at_most(n,2);