A381035 Numbers such that the least significant nonzero digit in their primorial base representation (A049345) is 1.

1, 2, 3, 5, 6, 7, 8, 9, 11, 13, 14, 15, 17, 19, 20, 21, 23, 25, 26, 27, 29, 30, 31, 32, 33, 35, 36, 37, 38, 39, 41, 43, 44, 45, 47, 49, 50, 51, 53, 55, 56, 57, 59, 61, 62, 63, 65, 66, 67, 68, 69, 71, 73, 74, 75, 77, 79, 80, 81, 83, 85, 86, 87, 89, 91, 92, 93, 95, 96, 97, 98, 99, 101, 103, 104, 105, 107, 109, 110, 111

Offset: 1

Author

Antti Karttunen, Feb 17 2025

Keywords

• nonn
• base
• easy

Comments

Numbers k such that A327860(k) is not a multiple of A053669(k), where A327860 is the arithmetic derivative of the primorial base exp-function, and A053669(k) gives the least prime not dividing k.

The asymptotic density of this sequence is 0.70523017... (A064648). - Amiram Eldar, Feb 17 2025

Examples

			   n, A049345(n), A276088(n)
  ---------------------------------------------
   4       20       2, thus 4 is not present,
  11      121       1, thus 11 is present,
  14      210       1, thus 14 is present.
		

Links

• Antti Karttunen, Table of n, a(n) for n = 1..20000
• Index entries for sequences related to primorial base.

Crossrefs

Complement of A380535 (apart from 0 which is in neither).

Cf. A049345, A064648, A276088, A380534.

Subsequences: A276156, A290249, A381034.

Programs

Mathematica

q[n_] := Module[{k = n, p = 2, r}, While[{k, r} = QuotientRemainder[k, p]; k > 0 && r == 0, p = NextPrime[p]]; r == 1]; Select[Range[120], q] (* Amiram Eldar, Feb 17 2025 *)

PARI

A276088(n) = { my(e=0, p=2); while(n && !(e=(n%p)), n = n/p; p = nextprime(1+p)); (e); };
is_A381035(n) = (1==A276088(n));

Formula

{k such that A276088(k) = 1}.