A370133 Numbers with no digit larger than 3 in primorial base, A049345.

0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74, 75, 76, 77, 78, 79, 80, 81, 82, 83, 90, 91, 92, 93, 94, 95, 96, 97, 98, 99

Offset: 1

Author

Antti Karttunen, Feb 11 2024

Keywords

• nonn
• base

Comments

Numbers k for which A328114(k) <= 3.

Numbers k such that A276086(k) is biquadratefree, A046100.

Links

• Antti Karttunen, Table of n, a(n) for n = 1..24576
• Index entries for sequences related to primorial base.

Crossrefs

Cf. A046100, A049345, A276086, A328114.

Cf. A369639 (nonsquarefree numbers whose arithmetic derivative is in this sequence).

Cf. A370132, A276156 (subsequences).

Subsequence of A351576: a(n) differs from A351576(n-1) for the first time at n=97, where a(97) = 210, while A351576(96) = 120, a term not present here.

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, ?(# > 3 &)] == 0]; Select[Range[0, 100], 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); };
isA370133(n) = ismaxprimobasedigit_at_most(n,3);