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A278959
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Length of the string that is generated by the concatenation of all the prime numbers < n (where n >= 0).
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1
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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
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refs;
listen;
history;
text;
internal format)
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OFFSET
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0,5
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COMMENTS
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In the following Python program, the algorithm based on the sieve of Eratosthenes is used to generate the primes.
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LINKS
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EXAMPLE
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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.
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MATHEMATICA
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Join[{0}, Accumulate[Table[If[PrimeQ[n], IntegerLength[n], 0], {n, 0, 60}]]] (* Harvey P. Dale, Mar 04 2023 *)
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PROG
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(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 str(i)+" "+str(p(i))
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CROSSREFS
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KEYWORD
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nonn,base
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AUTHOR
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STATUS
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approved
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