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Number of times most common final digit of primes appears in first n primes.
3

%I #14 Jul 23 2018 02:45:10

%S 1,1,1,1,1,2,2,2,3,3,3,3,3,4,4,5,5,5,5,5,6,6,7,7,7,7,8,8,8,9,9,9,9,9,

%T 9,9,10,10,11,11,11,11,11,12,12,12,12,13,13,13,14,14,14,14,14,15,15,

%U 15,15,15,16,17,17,17,18,18,18,18,19,19,19,19,20,20,20,21,21,21,21,21,21

%N Number of times most common final digit of primes appears in first n primes.

%H Robert Israel, <a href="/A063272/b063272.txt">Table of n, a(n) for n = 1..10000</a>

%H <a href="/index/Fi#final">Index entries for sequences related to final digits of numbers</a>

%F a(n) ~ n/phi(10) = n/4 by the Prime Number Theorem in Arithmetic Progressions. - _Charles R Greathouse IV_, Dec 29 2012

%e a(6)=2 since first six primes are 2,3,5,7,11,13, so most common final digit is 3 which has appeared twice.

%p V:= Vector(9):

%p p:= 1:

%p for n from 1 to 100 do

%p p:= nextprime(p);

%p r:= p mod 10;

%p V[r]:= V[r]+1;

%p A[n]:= max(V)

%p od:

%p seq(A[i],i=1..100); # _Robert Israel_, Jul 22 2018

%Y Cf. A000040, A007652, A063272. Slightly above floor(n/4), i.e., A002265.

%K base,nonn

%O 1,6

%A _Henry Bottomley_, Jul 13 2001