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

1,3

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).

Links

Rémy Sigrist, Table of n, a(n) for n = 1..10000

Index entries for sequences related to primorial base.

Example

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.

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 *)

Prog

(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))

Crossrefs

See A321682 for the factorial base variant.

Cf. A049345, A057588, A276150, A321682.

Sequence in context: A128215 A325676 A097132 * A321682 A013578 A283204

Adjacent sequences: A321680 A321681 A321682 * A321684 A321685 A321686

Keyword

nonn,base

Author

Rémy Sigrist, Nov 17 2018

Status

approved