cp's OEIS Frontend

A328585 Numbers n for which A257993(n) is equal to A257993(A276086(A276086(n))), where A276086 converts the primorial base expansion of n into its prime product form, and A257993 returns the index of the least prime not present in its argument.

%I A328585 #12 Oct 27 2019 17:31:16
%S A328585 1,3,5,6,7,9,11,13,15,17,18,19,21,23,25,27,29,31,33,35,36,37,39,41,43,
%T A328585 45,47,48,49,51,53,55,57,59,61,63,65,66,67,69,71,73,75,77,78,79,81,83,
%U A328585 85,87,89,91,93,95,96,97,99,101,103,105,107,108,109,111,113,115,117,119,121,123,125,126,127,129,131,133,135,137,138,139
%N A328585 Numbers n for which A257993(n) is equal to A257993(A276086(A276086(n))), where A276086 converts the primorial base expansion of n into its prime product form, and A257993 returns the index of the least prime not present in its argument.
%C A328585 Numbers n for which A257993(n) is equal to A328578(n).
%C A328585 All odd numbers are included, as A257993(2n+1) = A328578(2n+1) = 1 for all n >= 0.
%H A328585 Antti Karttunen, <a href="/A328585/b328585.txt">Table of n, a(n) for n = 1..10000</a>
%H A328585 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>
%o A328585 (PARI)
%o A328585 A257993(n) = { for(i=1,oo,if(n%prime(i),return(i))); }
%o A328585 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A328585 A328578(n) = A257993(A276086(A276086(n)));
%o A328585 isA328585(n) = (A328578(n) == A257993(n));
%Y A328585 Union of A005408 (odd numbers) and A328586 (even terms).
%Y A328585 Positions of zeros in A328590.
%Y A328585 Cf. A257993, A276086, A328578, A328587, A328588.
%Y A328585 Cf. also A328316, A328317.
%K A328585 nonn
%O A328585 1,2
%A A328585 _Antti Karttunen_, Oct 21 2019