%I #25 Jan 20 2024 04:05:00

%S 2,0,9,161,2189,29861,510221,1547371,79332523,9592991561,265257420749,

%T 1102527599503

%N a(n) is the least integer k whose arithmetic derivative is equal to the n-th primorial, or 0 if no such k exists.

%C a(n) = the smallest integer k for which A003415(k) = A002110(n), and 0 if no such k exists.

%C If there are non-Goldbachian solutions (A366890) for some n, i.e., if A369000(n) > 0, then the smallest of them appears here as a value of a(n).

%C a(12) <= 25962012375103, a(13) <= 4958985803436403, a(14) <= 32442711864461575, a(15) <= 11758779158543465383. - _David A. Corneth_, Jan 17 2024

%H Antti Karttunen, <a href="/A369000/a369000.txt">PARI program</a>

%H <a href="/index/Pri#primorial_numbers">Index entries for sequences related to primorial numbers</a>

%F a(n) <= A368704(n).

%F For n<>1, A003415(a(n)) = A002110(n).

%e a(0) = 2 as the least number k such that A003415(k) = A002110(0) = 1 is 2.

%e a(1) = 0 as there is no number k such that A003415(k) = A002110(1) = 2.

%e a(7) = 1547371 as it is the least number k such that A003415(k) = A002110(7) = 510510. See also A366890.

%Y Cf. A002110, A003415, A351029, A368704, A366890, A369000.

%Y Cf. also A369243.

%K nonn,more,hard

%O 0,1

%A _Antti Karttunen_, Jan 16 2024