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

%I A370133 #13 Mar 06 2024 00:59:54
%S A370133 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,
%T A370133 32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,60,
%U A370133 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
%N A370133 Numbers with no digit larger than 3 in primorial base, A049345.
%C A370133 Numbers k for which A328114(k) <= 3.
%C A370133 Numbers k such that A276086(k) is biquadratefree, A046100.
%H A370133 Antti Karttunen, <a href="/A370133/b370133.txt">Table of n, a(n) for n = 1..24576</a>
%H A370133 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%t A370133 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 *)
%o A370133 (PARI)
%o A370133 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); };
%o A370133 isA370133(n) = ismaxprimobasedigit_at_most(n,3);
%Y A370133 Cf. A046100, A049345, A276086, A328114.
%Y A370133 Cf. A369639 (nonsquarefree numbers whose arithmetic derivative is in this sequence).
%Y A370133 Cf. A370132, A276156 (subsequences).
%Y A370133 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.
%K A370133 nonn,base
%O A370133 1,3
%A A370133 _Antti Karttunen_, Feb 11 2024