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%I #53 Feb 03 2023 14:58:30
%S 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,
%T 46,49,52,55,58,61,64,67,70,73,76,79,82,85,88,91,94,97,100,103,106,
%U 109,112,115,118,121,124,127,130,133,136,139,142,145,148,151,154
%N Number of digits in the concatenation of first n primes.
%C Partial sums of A097944. - _Lekraj Beedassy_, Aug 26 2008
%H Charles R Greathouse IV, <a href="/A068670/b068670.txt">Table of n, a(n) for n = 0..10000</a>. (Initial 0 added by _M. F. Hasler_, Nov 02 2019.)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/Copeland-ErdosConstant.html">Copeland-Erdos Constant</a>
%F a(n) = Sum_{i=1..n} ceiling(log_10(1 + prime(i))). - _Daniel Forgues_, Apr 02 2014
%e a(5) is 6 because concatenating the first five primes gives 235711, which has six digits.
%t Table[n + Sum[Floor[Log[10, Prime[k]]], {k, 1, n}], {n, 1, 90}] (* Joseph Biberstine (jrbibers(AT)indiana.edu), Aug 12 2006 *)
%t Accumulate[IntegerLength[Prime[Range[70]]]] (* _Harvey P. Dale_, Jul 01 2012 *)
%o (Magma) a068670:=func< n | n + &+[ Floor(Log(10, NthPrime(k))): k in [1..n] ] >; [ a068670(n): n in [1..70] ];
%o (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
%o (Python)
%o from sympy import sieve
%o from itertools import accumulate, chain
%o def f(_, n): return _ + len(str(n))
%o def agen(): yield from accumulate(chain((0,), (p for p in sieve)), f)
%o print(list(islice(agen(), 62))) # _Michael S. Branicky_, Feb 03 2023
%Y Cf. A019518, A097944 (number of decimal digits of the primes).
%Y Cf. A033308 (decimal expansion of the Copeland-Erdos constant).
%K nonn,base
%O 0,3
%A Eugene McDonnell (eemcd(AT)mac.com), Jan 18 2004
%E Extended to a(0) = 0 by _M. F. Hasler_, Oct 24 2019
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