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A380535 Numbers such that the least significant nonzero digit in their primorial base representation (A049345) is greater than 1.

%I A380535 #14 Feb 18 2025 11:29:53
%S A380535 4,10,12,16,18,22,24,28,34,40,42,46,48,52,54,58,60,64,70,72,76,78,82,
%T A380535 84,88,90,94,100,102,106,108,112,114,118,120,124,130,132,136,138,142,
%U A380535 144,148,150,154,160,162,166,168,172,174,178,180,184,190,192,196,198,202,204,208,214,220,222,226,228,232,234,238,244,250
%N A380535 Numbers such that the least significant nonzero digit in their primorial base representation (A049345) is greater than 1.
%C A380535 Equally, numbers k such that A327860(k) [equally, A329029(k)] is a multiple of A053669(k), where A327860 is the arithmetic derivative of the primorial base exp-function, and A053669(k) gives the least prime not dividing k. See comments in A329029.
%C A380535 The asymptotic density of this sequence is 1 - A064648 = 0.294769828... . - _Amiram Eldar_, Feb 17 2025
%H A380535 Antti Karttunen, <a href="/A380535/b380535.txt">Table of n, a(n) for n = 1..20000</a>
%H A380535 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%F A380535 {k such that A276088(k) > 1}.
%e A380535    n, A049345(n), A276088(n)
%e A380535   ---------------------------------------------
%e A380535    4       20       2, thus 4 is present,
%e A380535   10      120       2, thus 10 is present,
%e A380535   11      121       1, thus 11 is not present,
%e A380535   12      200       2, thus 12 is present,
%e A380535   14      210       1, thus 14 is not present,
%e A380535   16      220       2, thus 16 is present,
%e A380535   18      300       3, thus 18 is present.
%t A380535 q[n_] := Module[{k = n, p = 2, r}, While[{k, r} = QuotientRemainder[k, p]; k > 0 && r == 0, p = NextPrime[p]]; r > 1]; Select[Range[250], q] (* _Amiram Eldar_, Feb 17 2025 *)
%o A380535 (PARI) is_A380535 = A380534;
%Y A380535 Cf. A049345, A053669, A064648, A276088, A327860, A329029, A380527, A380534 (characteristic function).
%Y A380535 Cf. also A342018.
%K A380535 nonn,base,easy
%O A380535 1,1
%A A380535 _Antti Karttunen_, Feb 11 2025