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

1,1

Links

Table of n, a(n) for n=1..48.

Formula

a(n) = A004427(A000043(n)). - Amiram Eldar, Oct 16 2024

Example

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, ...

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 *)

Crossrefs

Cf. A000043, A004427, A074464.

Sequence in context: A337008 A337007 A074464 * A038194 A111309 A007605

Adjacent sequences: A074460 A074461 A074462 * A074464 A074465 A074466

Keyword

nonn,base,more,changed

Author

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

Extensions

a(43)-a(47) from Ivan Panchenko, Aug 03 2018

a(48) from Amiram Eldar, Oct 16 2024

Status

approved