A083186 Sum of the first n primes whose indices are primes.
3, 8, 19, 36, 67, 108, 167, 234, 317, 426, 553, 710, 889, 1080, 1291, 1532, 1809, 2092, 2423, 2776, 3143, 3544, 3975, 4436, 4945, 5492, 6055, 6642, 7241, 7858, 8567, 9306, 10079, 10876, 11735, 12612, 13531, 14498, 15489, 16520, 17583, 18670, 19823
Offset: 1
Keywords
Links
- Amiram Eldar, Table of n, a(n) for n = 1..10000 (terms 1..1000 from Harvey P. Dale)
Programs
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Mathematica
Accumulate[Prime[Prime[Range[50]]]] (* Harvey P. Dale, Jun 24 2012 *)
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PARI
pipsum(n)=s=0; sr=0; for(x=1,n, y=prime(prime(x)); s+=y; print1(s" "); sr+=1.0/y; ); print(); print(sr)
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PARI
a(n)=my(i,j,s); forprime(p=2,, if(isprime(i++), s+=p; if(j++==n, return(s)))) \\ Charles R Greathouse IV, Oct 20 2015
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PARI
first(n)=my(v=vector(n),i,j,s); forprime(p=2,, if(isprime(i++), s+=p; v[j++]=s; if(j==n, return(v)))) \\ Charles R Greathouse IV, Oct 20 2015
Formula
a(n) = Sum_{k=1..n} prime(prime(k)).
a(n) ~ (n log n)^2 / 2. - Charles R Greathouse IV, Oct 20 2015
Comments