A368703 a(n) is the least integer k whose arithmetic derivative is equal to the n-th primorial, or 0 if no such k exists.

2, 0, 9, 161, 2189, 29861, 510221, 1547371, 79332523, 9592991561, 265257420749, 1102527599503

Offset: 0

Author

Antti Karttunen, Jan 16 2024

Keywords

• nonn
• more
• hard

Comments

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

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).

a(12) <= 25962012375103, a(13) <= 4958985803436403, a(14) <= 32442711864461575, a(15) <= 11758779158543465383. - David A. Corneth, Jan 17 2024

Examples

			a(0) = 2 as the least number k such that A003415(k) = A002110(0) = 1 is 2.
a(1) = 0 as there is no number k such that A003415(k) = A002110(1) = 2.
a(7) = 1547371 as it is the least number k such that A003415(k) = A002110(7) = 510510. See also A366890.
		

Links

• Antti Karttunen, PARI program
• Index entries for sequences related to primorial numbers

Crossrefs

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

Cf. also A369243.

Formula

a(n) <= A368704(n).

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