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A370133
Numbers with no digit larger than 3 in primorial base, A049345.
3
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.
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. 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
KEYWORD
nonn,base
AUTHOR
Antti Karttunen, Feb 11 2024
STATUS
approved