This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
Flatten[Position[Table[Total[Prime[Range[n,2n]]],{n,700}],?PrimeQ]] (* _Harvey P. Dale, Jun 10 2014 *)
36=6^2=A105720(3), 169=13^2=A105720(6), 247590225=15735^2=A105720(4072) No more terms up to 35746494200563714=A105720(34769014).
a=5;Do[a=a-Prime[n]+Prime[2n+1]+Prime[2n+2];If[IntegerQ[Sqrt[a]],Print[{a,n+1 }]],{n,1,10^8}];
[ NthPrime(2*n): n in [1..1000] ]; // Vincenzo Librandi, Apr 11 2011
A031215 := n->ithprime(2*n);
Table[ Prime[ 2n], {n, 52}] (* Robert G. Wilson v, Dec 01 2013 *)
a(n)=prime(2*n) \\ Charles R Greathouse IV, Jul 02 2013
Sum of 3rd prime to 5th prime = 5+7+11, hence a(3) = 23; sum of 4th prime to 7th prime = 7+11+13+17, hence a(4) = 48.
[ &+[ NthPrime(k): k in [n..2*n-1] ]: n in [1..44] ]; // Klaus Brockhaus, Jun 12 2009
nn=100;With[{prs=Prime[Range[nn]]},Table[Total[Take[prs,{n,2n-1}]],{n, Floor[(nn+1)/2]}]] (* Harvey P. Dale, Jan 12 2014 *)
For n=7, prime(7) = 17 and starting there 2 primes 17 + 19 = 36 which is square, so that a(7)=2.
f:= proc(n) local p,s,k;
p:= ithprime(n); s:= p;
for k from 2 do
p:= nextprime(p);
s:= s+p;
if issqr(s) then return k fi
od
end proc:
map(f, [$1..36]); # Robert Israel, Nov 08 2022
a[n_] := Module[{p = s = Prime[n], k = 1}, While[! IntegerQ[Sqrt[s]], p = NextPrime[p]; s += p; k++]; k]; Array[a, 36] (* Amiram Eldar, Nov 08 2022 *)
Comments