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A266991 Smallest representatives of primes of distinct digital types. 2
2, 11, 13, 101, 103, 113, 199, 1009, 1013, 1021, 1033, 1039, 1103, 1117, 1151, 1303, 1511, 1777, 10007, 10037, 10061, 10099, 10103, 10111, 10133, 10139, 10141, 10211, 10223, 10243, 10271, 10301, 10303, 10313, 10331, 10333, 10343, 10399, 10513, 10607, 11003 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Numbers of different digital types for n-digit primes are 1,2,4,11,...

LINKS

Peter J. C. Moses, Table of n, a(n) for n = 1..5000

EXAMPLE

The first 3-digit prime is 101=a(4).

The following 3-digit prime is 103. It does not have the same digital type as 101, since in 103 there are 3 distinct digits, but not in 101. So a(5)=103.

The next two primes 107 and 109 belongs to type 103.

Next consider 113. Here the first two digits are the same, but in 101 and 103 they are not. So 113 is a new type, and a(6)=113.

It remains to find the smallest prime of form XYY. It is 199=a(7).

Now we see that every 3-digit prime is of one of the 4 types a(4),a(5),a(6),a(7).

Next we consider the first 4-digit number a(8)=1009, etc.

CROSSREFS

Cf. A264406, A266946.

Sequence in context: A042563 A041163 A073914 * A041971 A299531 A106660

Adjacent sequences:  A266988 A266989 A266990 * A266992 A266993 A266994

KEYWORD

nonn,base

AUTHOR

Vladimir Shevelev, Jan 08 2016

EXTENSIONS

More terms from Peter J. C. Moses, Jan 08 2016

STATUS

approved

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Last modified January 20 05:19 EST 2020. Contains 331067 sequences. (Running on oeis4.)