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

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, 14, 16, 16, 18, 18, 18, 18, 18, 18, 20, 20, 20, 20, 22, 22, 24, 24, 24, 24, 26, 26, 26, 26, 26, 26, 28, 28, 28, 28, 28, 28, 30

Offset: 0

Author

Indranil Ghosh, Dec 02 2016

Keywords

• nonn
• base

Comments

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

Examples

			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.
		

Links

• Indranil Ghosh, Table of n, a(n) for n = 0..100000
• Wikipedia, Sieve Of Eratosthenes

Crossrefs

Cf. A000040, A068670, A097944.

Programs

Mathematica

Join[{0},Accumulate[Table[If[PrimeQ[n],IntegerLength[n],0],{n,0,60}]]] (* Harvey P. Dale, Mar 04 2023 *)

Python

def p(n):
    if n<=2:
        return 0
    s=1
    l = [True] * n
    for i in range(3,int(n**0.5)+1,2):
        if l[i]:
            l[i*i::2*i]=[False]*((n-i*i-1)//(2*i)+1)
    for i in range(3,n,2):
            if l[i]:
                s+=len(str(i))
    return s
for i in range(0, 100001):
    print(f'{i} {p(i)}')