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Length of the string that is generated by the concatenation of all the prime numbers < n (where n >= 0).
1

%I #32 Nov 13 2024 16:41:24

%S 0,0,0,1,2,2,3,3,4,4,4,4,6,6,8,8,8,8,10,10,12,12,12,12,14,14,14,14,14,

%T 14,16,16,18,18,18,18,18,18,20,20,20,20,22,22,24,24,24,24,26,26,26,26,

%U 26,26,28,28,28,28,28,28,30

%N Length of the string that is generated by the concatenation of all the prime numbers < n (where n >= 0).

%C In the following Python program, the algorithm based on the sieve of Eratosthenes is used to generate the primes.

%H Indranil Ghosh, <a href="/A278959/b278959.txt">Table of n, a(n) for n = 0..100000</a>

%H Wikipedia, <a href="https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes">Sieve Of Eratosthenes</a>

%e For n=15, the primes < n are 2,3,5,7,11,13. So the concatenated string is "23571113", which has length=8. a(n)=8.

%t Join[{0},Accumulate[Table[If[PrimeQ[n],IntegerLength[n],0],{n,0,60}]]] (* _Harvey P. Dale_, Mar 04 2023 *)

%o (Python)

%o def p(n):

%o if n<=2:

%o return 0

%o s=1

%o l = [True] * n

%o for i in range(3,int(n**0.5)+1,2):

%o if l[i]:

%o l[i*i::2*i]=[False]*((n-i*i-1)//(2*i)+1)

%o for i in range(3,n,2):

%o if l[i]:

%o s+=len(str(i))

%o return s

%o for i in range(0, 100001):

%o print(f'{i} {p(i)}')

%Y Cf. A000040, A068670, A097944.

%K nonn,base

%O 0,5

%A _Indranil Ghosh_, Dec 02 2016