A097944 Number of digits in n-th prime.

1, 1, 1, 1, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 2, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3, 3

Offset

1,5

Comments

For primes p <= n sum(a(n)) -> n/2 and n-> inf.

Links

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Formula

a(n) = (log n + log log n)/(log 10) + O(1).

a(n) = A055642(A000040(n)). - Reinhard Zumkeller, Apr 08 2012

a(n) = A068670(n) - A068670(n-1). - M. F. Hasler, Oct 24 2019

Example

The first 4 primes are 2,3,5,7. These are 1-digit numbers so the first 4 entries in the table are 1's.

Mathematica

a[n_]:=StringLength[ToString[Prime[n]]]; (* Vladimir Joseph Stephan Orlovsky, Dec 03 2008 *)
IntegerLength[Prime[Range[110]]] (* Harvey P. Dale, Oct 04 2012 *)

Prog

(PARI) a(n)=#Str(prime(n))
(PARI) A097944(n)=logint(prime(n), 10)+1 \\ M. F. Hasler, Oct 24 2019
(Haskell)
a097944 = a055642 . a000040 -- Reinhard Zumkeller, Apr 08 2012

Crossrefs

Cf. A060417, A068670 (partial sums).

Sequence in context: A204553 A214455 A060417 * A037203 A032556 A110592

Adjacent sequences: A097941 A097942 A097943 * A097945 A097946 A097947

Keyword

nonn,base,easy

Author

Cino Hilliard, Sep 05 2004

Status

approved