A220076 - OEIS

A220076

Numbers with exactly six distinct base-10 digits.

102345, 102346, 102347, 102348, 102349, 102354, 102356, 102357, 102358, 102359, 102364, 102365, 102367, 102368, 102369, 102374, 102375, 102376, 102378, 102379, 102384, 102385, 102386, 102387, 102389, 102394, 102395, 102396, 102397, 102398, 102435, 102436

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OFFSET

1,1

COMMENTS

This is to A031969 as 6 is to 4. This is the 6th row of the array A(k,n) = n-th number in which the number of distinct base-10 digits is k. A031969 is the 4th row. A220063 is the 5th row. Pandigital numbers A050278 is the 10th row. The subsequence of primes begins: 102359, 102367, 102397, 102437.

There are 9*9!/4! = 136080 terms with 6 digits. After the first 9!/4! = 15120 terms with leading digit 1, follow the same numbers with digits 1 and 2 exchanged, and then similar with leading digits 3 through 9, each time simply exchanged with the previous leading digit in the entire block of 15120 numbers. After a(136080) = 987654 start the 7-digit terms with a(136081) = 1002345 = a(1) + 9*10^5, see formula. - M. F. Hasler, Apr 09 2026

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..10000

FORMULA

a(136080 + n) = a(n) + 9*10^5 for 0 < n < 1681, and the same terms + 10^4 for 1680 < n < 3361. - M. F. Hasler, Apr 09 2026

MATHEMATICA

Select[Range[100000, 103000], Length[Union[IntegerDigits[#]]] == 6 &] (* T. D. Noe, Dec 04 2012 *)

PROG

(Magma) a:=[n: n in [100000..102500] | #Seqset(Intseq(n, 10)) eq 6]; a; // Vincenzo Librandi, Apr 09 2026

CROSSREFS

Cf. A031969, A050278, A220063.

Sequence in context: A186088 A186087 A106814 * A235694 A235158 A074669

Adjacent sequences: A220073 A220074 A220075 * A220077 A220078 A220079