A266991 Smallest representatives of primes of distinct digital types.

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

Offset: 1

Author

Vladimir Shevelev, Jan 08 2016

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

Links

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

Crossrefs

Cf. A264406, A266946.

Extensions

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