A098227 Number of primes with exactly n decimal digits which have repeated digits.

0, 1, 46, 551, 5834, 58667, 552131, 5006366, 44940852, 404204977, 3663002302, 33489857205, 308457624821, 2858876213963, 26639628671867, 249393770611256, 2344318816620308, 22116397130086627, 209317712988603747

Offset

1,3

Comments

Above n = 9, a(n) = A006879(n) because above 10 there must be repeated digits. At n = 10 the sum of digits 0+1+2+3+4+5+6+7+8+9=45 is divisible by 3, so no primes with 10 distinct decimal digits exist, all primes must have repeated digits.

Links

Table of n, a(n) for n=1..19.

Example

Above n = 9 a(n) = A006879(n) because above 10 there must be a repetition. At n = 10 the sum of digits 0+1+2+3+4+5+6+7+8+9=45 is divisible by 3, so no primes with 10 distinct decimal digits exist.

Mathematica

Table[Count[Prime@ Range[If[# == 0, 1, # + 1] &@ PrimePi[10^n], PrimePi[10^(n + 1) - 1]], p_ /; Total@ Boole@ Map[# > 1 &, DigitCount@ p] > 0], {n, 0, 6}] (* Michael De Vlieger, Mar 26 2017 *)

Crossrefs

Cf. A006880, A006879, A098224-A098226.

Sequence in context: A223914 A224186 A027940 * A077732 A200898 A160151

Adjacent sequences: A098224 A098225 A098226 * A098228 A098229 A098230

Keyword

base,nonn

Author

Labos Elemer, Oct 25 2004

Status

approved