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.

0, 1, 2, 6, 26, 95, 122, 185, 206, 1382, 1919, 2006, 2285, 2306, 2966, 4681, 4841, 5909, 13961, 14269, 21446, 30026, 34249, 37231, 54589, 54611, 61459, 90065, 135229, 145309, 204566, 217621, 262099, 266950, 289621, 306302, 310939, 341699, 350099, 353779, 356809, 358091, 364361, 496751, 501289, 503669, 510506, 515059

Offset: 1

Author

Antti Karttunen, May 15 2025

Keywords

• nonn
• base

Examples

			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.
2 is a term as A003415(2) = 1, with A049345(1) = 1, which is a suffix of A049345(A276086(2)) = 11.
6 is a term as A003415(6) = 5, with A049345(5) = 21, which is a suffix of A049345(A276086(6)) = 21.
95 is a term as A003415(95) = 24, with A049345(24) = 400, which is a suffix of A049345(A276086(95)) = 272400.
		

Links

• Index entries for sequences related to primorial base.

Crossrefs

Subsequence of A383303.

Cf. A003415, A049345, A276086, A276087.

Cf. also A383300.

Programs

PARI

A003415(n) = if(n<=1, 0, my(f=factor(n)); n*sum(i=1, #f~, f[i, 2]/f[i, 1]));
A276086(n) = { my(m=1, p=2); while(n, m *= (p^(n%p)); n = n\p; p = nextprime(1+p)); (m); };
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); };