cp's OEIS Frontend

A383933 Numbers k such that primorial base expansion of A276086(k) has the primorial base expansion of A003415(k) as its suffix, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.

%I A383933 #8 May 15 2025 17:11:45
%S A383933 0,1,2,6,26,95,122,185,206,1382,1919,2006,2285,2306,2966,4681,4841,
%T A383933 5909,13961,14269,21446,30026,34249,37231,54589,54611,61459,90065,
%U A383933 135229,145309,204566,217621,262099,266950,289621,306302,310939,341699,350099,353779,356809,358091,364361,496751,501289,503669,510506,515059
%N A383933 Numbers k such that primorial base expansion of A276086(k) has the primorial base expansion of A003415(k) as its suffix, where A003415 is the arithmetic derivative, and A276086 is the primorial base exp-function.
%H A383933 <a href="/index/Pri#primorialbase">Index entries for sequences related to primorial base</a>.
%e A383933 0 and 1 are terms as A003415(0) = A003415(1) = 0, whose primorial base expansion is here understood as an empty sequence of digits, thus occurring as a suffix of all representations.
%e A383933 2 is a term as A003415(2) = 1, with A049345(1) = 1, which is a suffix of A049345(A276086(2)) = 11.
%e A383933 6 is a term as A003415(6) = 5, with A049345(5) = 21, which is a suffix of A049345(A276086(6)) = 21.
%e A383933 95 is a term as A003415(95) = 24, with A049345(24) = 400, which is a suffix of A049345(A276086(95)) = 272400.
%o A383933 (PARI)
%o A383933 A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
%o A383933 A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
%o A383933 isA383933(n) = { my(p=2, k=A003415(n)); n = A276086(n); while(k, if((k%p)!=(n%p), return(0)); n = n\p; k = k\p; p = nextprime(1+p)); (1); };
%Y A383933 Subsequence of A383303.
%Y A383933 Cf. A003415, A049345, A276086, A276087.
%Y A383933 Cf. also A383300.
%K A383933 nonn,base
%O A383933 1,3
%A A383933 _Antti Karttunen_, May 15 2025