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A321683
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Numbers with distinct digits in primorial base.
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3
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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
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OFFSET
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1,3
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COMMENTS
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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).
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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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 *)
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PROG
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(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))
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CROSSREFS
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See A321682 for the factorial base variant.
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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