A380535 Numbers such that the least significant nonzero digit in their primorial base representation (A049345) is greater than 1.

4, 10, 12, 16, 18, 22, 24, 28, 34, 40, 42, 46, 48, 52, 54, 58, 60, 64, 70, 72, 76, 78, 82, 84, 88, 90, 94, 100, 102, 106, 108, 112, 114, 118, 120, 124, 130, 132, 136, 138, 142, 144, 148, 150, 154, 160, 162, 166, 168, 172, 174, 178, 180, 184, 190, 192, 196, 198, 202, 204, 208, 214, 220, 222, 226, 228, 232, 234, 238, 244, 250

Offset: 1

Author

Antti Karttunen, Feb 11 2025

Keywords

• nonn
• base
• easy

Comments

Equally, numbers k such that A327860(k) [equally, A329029(k)] is 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. See comments in A329029.

The asymptotic density of this sequence is 1 - A064648 = 0.294769828... . - Amiram Eldar, Feb 17 2025

Examples

			   n, A049345(n), A276088(n)
  ---------------------------------------------
   4       20       2, thus 4 is present,
  10      120       2, thus 10 is present,
  11      121       1, thus 11 is not present,
  12      200       2, thus 12 is present,
  14      210       1, thus 14 is not present,
  16      220       2, thus 16 is present,
  18      300       3, thus 18 is present.
		

Links

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

Crossrefs

Cf. A049345, A053669, A064648, A276088, A327860, A329029, A380527, A380534 (characteristic function).

Cf. also A342018.

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[250], q] (* Amiram Eldar, Feb 17 2025 *)

PARI

is_A380535 = A380534;

Formula

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