A074463 Average digit (rounded up) in the decimal expansion of a prime number p, where 2^p-1 is a Mersenne prime.
2, 3, 5, 7, 2, 4, 5, 2, 4, 9, 3, 4, 3, 5, 5, 2, 4, 4, 4, 4, 8, 6, 2, 6, 3, 4, 6, 5, 2, 4, 4, 7, 6, 6, 6, 5, 4, 6, 5, 4, 4, 6, 4, 5, 6, 4, 4, 6
Offset: 1
Examples
Prime numbers for Mersenne: 2, 3, 5, 7, 13, 17, 19, 31, 61, ..., so the averages of digits rounded up are 2, 3, 5, 7, (1+3)/2=2, (1+7)/2=4, (1+9)/2=5, (3+1)/2=2, ceiling((6+1)/2)=4, ...
Programs
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Mathematica
f[n_] := Block[{id = IntegerDigits@ n}, Ceiling[Plus @@ id/Length@ id]]; lst = { (* terms from A000043 *) }; f@# & /@ lst (* Robert G. Wilson v, Jun 26 2013 *) Ceiling[Mean[IntegerDigits[#]]]&/@MersennePrimeExponent[Range[47]] (* Harvey P. Dale, Feb 01 2023 *)
Formula
Extensions
a(43)-a(47) from Ivan Panchenko, Aug 03 2018
a(48) from Amiram Eldar, Oct 16 2024