A297062 -id:A297062

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A297065

Starting with a(1) = 0, a(2) = 1, a(n) = smallest nonnegative integer not yet in the sequence that shares all digits with previous terms.

+10
4

0, 1, 10, 100, 101, 102, 120, 201, 210, 1002, 1012, 1020, 1021, 1022, 1023, 1032, 1203, 1230, 1302, 1320, 2013, 2031, 2103, 2130, 2301, 2310, 3012, 3021, 3102, 3120, 3201, 3210, 10234, 10243, 10324, 10342, 10423, 10432, 12034, 12043, 12304, 12340, 12403, 12430, 13024

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

COMMENTS

Without the restriction that no repeated digits are allowed (as in A297062), the sequence is infinite.

The smallest 10-digit term is 1023456789, the largest 10-digit term is 9876543210, and digits not contained in previous terms are introduced at n = 6, 15, 33, 129, 729, 5049, 40329, 362889.

LINKS

Table of n, a(n) for n=1..45.

EXAMPLE

a(6)=102 and not 110 since 102 < 110, hence the digit 2 is introduced at n=6.

CROSSREFS

Cf. A297062.

KEYWORD

base,nonn

AUTHOR

Enrique Navarrete, Dec 24 2017

STATUS

approved

A199168

Numbers whose digits are a permutation of (0,...,m) for some m.

+10
1

0, 10, 102, 120, 201, 210, 1023, 1032, 1203, 1230, 1302, 1320, 2013, 2031, 2103, 2130, 2301, 2310, 3012, 3021, 3102, 3120, 3201, 3210, 10234, 10243, 10324, 10342, 10423, 10432, 12034, 12043, 12304, 12340, 12403, 12430, 13024, 13042, 13204, 13240, 13402, 13420

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

COMMENTS

2013 is the fourth odd term in this sequence: Up to and including the 5 digit terms, odd terms must end in 1 or 3.

Due to the fact that 0 is not allowed as initial digit, this sequence is quite different from A030299, the analog with digits (1,...,m) instead of (0,...,m).

LINKS

Table of n, a(n) for n=1..42.

PROG

(PARI) n_digit_terms(n)={my(a=[], p=vector(n, i, 10^(n-i))~); for(i=(n-1)!, n!-(n>1), a=concat(a, numtoperm(n, i)%n*p)); vecsort(a)} \\ - M. F. Hasler, Jan 08 2013

CROSSREFS

Cf. A187796 (subset of primes), A203569 (also a subset), A030299 (permutations of 1..m) and references therein.

Pandigital numbers A050278 are also a subset.

Cf. A297062.

KEYWORD

nonn,base,easy

AUTHOR

M. F. Hasler, Jan 08 2013

STATUS

approved

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