A097944 - OEIS

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A097944

Number of digits in n-th prime.

9

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

(list; graph; refs; listen; history; text; internal format)

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