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Average digit (rounded up) in the decimal expansion of prime(n).
3

%I #18 Nov 06 2022 18:35:43

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

%T 5,3,5,4,5,4,6,4,4,5,6,7,2,3,4,5,3,5,3,3,5,4,6,4,6,4,5,5,4,2,3,4,3,5,

%U 5,6,4,6,6,5,7,5,7,7,2,5,5,3,3,4,6,4,6,6,4,5,6,7,7,5,8,3,5,3,4,4,6,6,5,7,5,7,7,6,8,3,5,4,5,6,4,4,5,6,5,7

%N Average digit (rounded up) in the decimal expansion of prime(n).

%F a(n) = ceiling(A007605(n)/A097944(n)). - _R. J. Mathar_, Sep 23 2008

%F a(n) = A004427(A000040(n)). - _Reinhard Zumkeller_, May 27 2010

%e The prime numbers begin with 2,3,5,7,11,13,17,19,23,... so the average digits rounded up are 2, 3, 5, 7, (1+1)/2=1, (1+3)/2=2, (1+7)/2=4, (1+9)/2=5, ceiling((2+3)/2)=3, ...

%t Table[Ceiling[Mean[IntegerDigits[p]]],{p,Prime[Range[120]]}] (* _Harvey P. Dale_, Nov 06 2022 *)

%o (PARI) a(n) = my(d=digits(prime(n))); ceil(vecsum(d)/#d); \\ _Michel Marcus_, Apr 23 2022

%Y Cf. A000040, A004427, A074461, A073342.

%Y Cf. A007605, A097944.

%K easy,nonn,base

%O 1,1

%A Y. Kelly Itakura (yitkr(AT)mta.ca), Aug 23 2002

%E Offset changed to 1, cf. to A073342 added, and extended by _R. J. Mathar_, Sep 23 2008