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A068670
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Number of digits in the concatenation of first n primes.
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11
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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
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0,3
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COMMENTS
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LINKS
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FORMULA
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a(n) = Sum_{i=1..n} ceiling(log_10(1 + prime(i))). - Daniel Forgues, Apr 02 2014
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EXAMPLE
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a(5) is 6 because concatenating the first five primes gives 235711, which has six digits.
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MATHEMATICA
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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 *)
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PROG
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(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
(Python)
from sympy import sieve
from itertools import accumulate, chain
def f(_, n): return _ + len(str(n))
def agen(): yield from accumulate(chain((0, ), (p for p in sieve)), f)
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CROSSREFS
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Cf. A033308 (decimal expansion of the Copeland-Erdos constant).
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KEYWORD
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nonn,base
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AUTHOR
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Eugene McDonnell (eemcd(AT)mac.com), Jan 18 2004
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EXTENSIONS
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STATUS
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approved
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