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A098227 Number of primes with exactly n decimal digits which have repeated digits. 5

%I #8 Mar 26 2017 23:10:52

%S 0,1,46,551,5834,58667,552131,5006366,44940852,404204977,3663002302,

%T 33489857205,308457624821,2858876213963,26639628671867,

%U 249393770611256,2344318816620308,22116397130086627,209317712988603747

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

%C 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.

%e 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.

%t 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 *)

%Y Cf. A006880, A006879, A098224-A098226.

%K base,nonn

%O 1,3

%A _Labos Elemer_, Oct 25 2004

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Last modified April 25 12:33 EDT 2024. Contains 371969 sequences. (Running on oeis4.)