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A381035 Numbers such that the least significant nonzero digit in their primorial base representation (A049345) is 1.

%I A381035 #12 Feb 18 2025 19:02:07
%S A381035 1,2,3,5,6,7,8,9,11,13,14,15,17,19,20,21,23,25,26,27,29,30,31,32,33,
%T A381035 35,36,37,38,39,41,43,44,45,47,49,50,51,53,55,56,57,59,61,62,63,65,66,
%U A381035 67,68,69,71,73,74,75,77,79,80,81,83,85,86,87,89,91,92,93,95,96,97,98,99,101,103,104,105,107,109,110,111
%N A381035 Numbers such that the least significant nonzero digit in their primorial base representation (A049345) is 1.
%C A381035 Numbers k such that A327860(k) is not 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.
%C A381035 The asymptotic density of this sequence is 0.70523017... (A064648). - _Amiram Eldar_, Feb 17 2025
%H A381035 Antti Karttunen, <a href="/A381035/b381035.txt">Table of n, a(n) for n = 1..20000</a>
%H A381035 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%F A381035 {k such that A276088(k) = 1}.
%e A381035    n, A049345(n), A276088(n)
%e A381035   ---------------------------------------------
%e A381035    4       20       2, thus 4 is not present,
%e A381035   11      121       1, thus 11 is present,
%e A381035   14      210       1, thus 14 is present.
%t A381035 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[120], q] (* _Amiram Eldar_, Feb 17 2025 *)
%o A381035 (PARI)
%o A381035 A276088(n) = { my(e=0, p=2); while(n && !(e=(n%p)), n = n/p; p = nextprime(1+p)); (e); };
%o A381035 is_A381035(n) = (1==A276088(n));
%Y A381035 Complement of A380535 (apart from 0 which is in neither).
%Y A381035 Cf. A049345, A064648, A276088, A380534.
%Y A381035 Subsequences: A276156, A290249, A381034.
%K A381035 nonn,base,easy
%O A381035 1,2
%A A381035 _Antti Karttunen_, Feb 17 2025