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A278959 Length of the string that is generated by the concatenation of all the prime numbers < n (where n >= 0).

%I A278959 #32 Nov 13 2024 16:41:24
%S A278959 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 A278959 14,16,16,18,18,18,18,18,18,20,20,20,20,22,22,24,24,24,24,26,26,26,26,
%U A278959 26,26,28,28,28,28,28,28,30
%N A278959 Length of the string that is generated by the concatenation of all the prime numbers < n (where n >= 0).
%C A278959 In the following Python program, the algorithm based on the sieve of Eratosthenes is used to generate the primes.
%H A278959 Indranil Ghosh, <a href="/A278959/b278959.txt">Table of n, a(n) for n = 0..100000</a>
%H A278959 Wikipedia, <a href="https://en.wikipedia.org/wiki/Sieve_of_Eratosthenes">Sieve Of Eratosthenes</a>
%e A278959 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 A278959 Join[{0},Accumulate[Table[If[PrimeQ[n],IntegerLength[n],0],{n,0,60}]]] (* _Harvey P. Dale_, Mar 04 2023 *)
%o A278959 (Python)
%o A278959 def p(n):
%o A278959     if n<=2:
%o A278959         return 0
%o A278959     s=1
%o A278959     l = [True] * n
%o A278959     for i in range(3,int(n**0.5)+1,2):
%o A278959         if l[i]:
%o A278959             l[i*i::2*i]=[False]*((n-i*i-1)//(2*i)+1)
%o A278959     for i in range(3,n,2):
%o A278959             if l[i]:
%o A278959                 s+=len(str(i))
%o A278959     return s
%o A278959 for i in range(0, 100001):
%o A278959     print(f'{i} {p(i)}')
%Y A278959 Cf. A000040, A068670, A097944.
%K A278959 nonn,base
%O A278959 0,5
%A A278959 _Indranil Ghosh_, Dec 02 2016