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

1,3

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.

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 *)

Prog

(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);

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.

Sequence in context: A272076 A335280 A335282 * A351576 A132264 A214922

Adjacent sequences: A370130 A370131 A370132 * A370134 A370135 A370136

Keyword

nonn,base

Author

Antti Karttunen, Feb 11 2024

Status

approved