

A068670


Number of digits in the concatenation of first n primes.


10



0, 1, 2, 3, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24, 26, 28, 30, 32, 34, 36, 38, 40, 42, 44, 46, 49, 52, 55, 58, 61, 64, 67, 70, 73, 76, 79, 82, 85, 88, 91, 94, 97, 100, 103, 106, 109, 112, 115, 118, 121, 124, 127, 130, 133, 136, 139, 142, 145, 148, 151, 154
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OFFSET

0,3


COMMENTS

Partial sums of A097944.  Lekraj Beedassy, Aug 26 2008


LINKS

Charles R Greathouse IV, Table of n, a(n) for n = 0..10000. (Initial 0 added by M. F. Hasler, Nov 02 2019.)
Eric Weisstein's World of Mathematics, CopelandErdos Constant


FORMULA

a(n) = Sum_{i=1..n} ceiling(log_10(1 + prime(i))).  Daniel Forgues, Apr 02 2014


EXAMPLE

a(5) is 6 because concatenating the first five primes gives 235711, which has six digits.


MATHEMATICA

Table[n + Sum[Floor[Log[10, Prime[k]]], {k, 1, n}], {n, 1, 90}] (* Joseph Biberstine (jrbibers(AT)indiana.edu), Aug 12 2006 *)
Accumulate[IntegerLength[Prime[Range[70]]]] (* Harvey P. Dale, Jul 01 2012 *)


PROG

(MAGMA) a068670:=func< n  n + &+[ Floor(Log(10, NthPrime(k))): k in [1..n] ] >; [ a068670(n): n in [1..70] ];
(PARI) A68670=List(0); A068670(n)={for(N=#A68670, n, listput(A68670, A68670[N] + A097944(N))); A68670[n+1]} \\ M. F. Hasler, Oct 24 2019


CROSSREFS

Cf. A019518, A097944 (number of decimal digits of the primes).
Cf. A033308 (decimal expansion of the CopelandErdos constant).
Sequence in context: A158023 A004271 A004278 * A084925 A045718 A068005
Adjacent sequences: A068667 A068668 A068669 * A068671 A068672 A068673


KEYWORD

nonn,base


AUTHOR

Eugene McDonnell (eemcd(AT)mac.com), Jan 18 2004


EXTENSIONS

Extended to a(0) = 0 by M. F. Hasler, Oct 24 2019


STATUS

approved



