A369243 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.

2, 0, 14, 45, 198, 5114, 65174, 1086194, 20485574, 465779078, 0, 293420849770, 318745032938881, 256934628877545, 26789279193702134

Offset

0,1

Comments

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

Links

Table of n, a(n) for n=0..14.

Antti Karttunen, PARI program for computing terms of this and related sequences.

Formula

a(n) <= A369244(n).

a(n) = A369240(n,1) if A369239(n) > 0; otherwise a(n) = 0. - Max Alekseyev, Sep 17 2025

Example

a(0) = 2 as the least number k such that A003415(k) = A143293(0) = 1 is 2.
a(1) = 0 as there is no number k such that A003415(k) = A143293(1) = 3.

Crossrefs

Cf. A003415, A143293, A369239, A369240, A369244, A368703.

Sequence in context: A064855 A088504 A229091 * A189425 A266169 A277928

Adjacent sequences: A369240 A369241 A369242 * A369244 A369245 A369246

Keyword

nonn,hard,more

Author

Antti Karttunen, Jan 19 2024

Extensions

a(13)-a(14) from Max Alekseyev, Oct 11 2025

Status

approved