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a(n) is the least integer k whose arithmetic derivative is equal to the n-th partial sum of primorials, and 0 if no such k exists.
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%I #10 Jan 21 2024 18:09:49

%S 2,0,14,45,198,5114,65174,1086194,20485574,465779078,0,293420849770,

%T 318745032938881

%N a(n) is the least integer k whose arithmetic derivative is equal to the n-th partial sum of primorials, and 0 if no such k exists.

%C a(n) = the smallest integer k for which A003415(k) = A143293(n), and 0 if no such k exists.

%H Antti Karttunen, <a href="/A369239/a369239.txt">PARI program for computing terms of this and related sequences</a>.

%F a(n) <= A369244(n).

%e a(0) = 2 as the least number k such that A003415(k) = A143293(0) = 1 is 2.

%e a(1) = 0 as there is no number k such that A003415(k) = A143293(1) = 3.

%Y Cf. A003415, A143293, A369244.

%Y Cf also A368703.

%K nonn,hard,more

%O 0,1

%A _Antti Karttunen_, Jan 19 2024