A267013 Number of distinct digital types of n-digit primes in base 10.

1, 2, 4, 11, 51, 177, 876, 3965, 20782, 114459

Offset

1,2

Comments

The sequence is related to A266991.

Sequence {A164864(n) - a(n)}_(n>=1) begins 0,0,1,4,1,26,1,175,365,1516,...

One can explain, why, for example, a(4)=11, instead of A164864(4)=15. There exist exactly 4 types of 4-digit numbers, which cannot be prime. In A266946 these types are: 1001, 1010, 1100, 1111. Indeed, numbers abba,aabb,aaaa are divisible by 11; a number abab is divisible by 101.

In other cases of n-digit types we should verify the divisibility of numbers of types in A266946 at least by primes of the form 11,101,... Besides, a digital type 1...1 exists only for n in A004023, i.e., for only 9 values of n from the first 270343. This simplifies the calculations.

Links

Table of n, a(n) for n=1..10.

Crossrefs

Cf. A164864, A164904, A264406, A266946.

Sequence in context: A068488 A096119 A117157 * A318532 A057857 A352969

Adjacent sequences: A267010 A267011 A267012 * A267014 A267015 A267016

Keyword

nonn,base,more

Author

Vladimir Shevelev and Peter J. C. Moses, Jan 08 2016

Status

approved