A321683 Numbers with distinct digits in primorial base.

0, 1, 2, 4, 5, 10, 13, 14, 19, 20, 22, 23, 25, 26, 28, 29, 52, 58, 79, 80, 85, 86, 95, 100, 103, 104, 115, 116, 118, 119, 125, 130, 133, 134, 139, 140, 142, 143, 155, 160, 163, 164, 169, 170, 172, 173, 175, 176, 178, 179, 185, 190, 193, 194, 199, 200, 202, 203

Offset: 1

Author

Rémy Sigrist, Nov 17 2018

Keywords

• nonn
• base

Comments

This sequence is a variant of A010784 (numbers with distinct digits in decimal). The final term of that sequence is 9876543210. This sequence, by contrast, has infinitely many terms (for example, all the terms of A057588 belong to this sequence).

Examples

			13 in primorial base is 201, which has no repeated digits, hence 13 is in the sequence.
14 in primorial base is 210, which has no repeated digits, hence 14 is also in the sequence.
15 in primorial base is 211, so 15 is not in the sequence on account of the digit 1 appearing twice in its primorial base representation.
		

Links

• Rémy Sigrist, Table of n, a(n) for n = 1..10000
• Index entries for sequences related to primorial base.

Crossrefs

See A321682 for the factorial base variant.

Cf. A049345, A057588, A276150, A321682.

Programs

Mathematica

q[n_] := Module[{k = n, p = 2, s = {}, r}, While[{k, r} = QuotientRemainder[k, p]; k != 0 || r != 0, AppendTo[s, r]; p = NextPrime[p]]; UnsameQ @@ s]; Select[Range[0, 210], q] (* Amiram Eldar, Mar 13 2024 *)

PARI

is(n) = my (s=0); forprime (p=2, oo, if (n==0, return (1)); my (d=n%p); if (bittest(s,d), return (0), s+=2^d; n\=p))