A175037 - OEIS

%I #7 Apr 06 2018 17:43:38

%S 12,83,228,1265,1321,5068,3617,11993,32245,14404,65873,67182,35224,

%T 93088,201244,245920,115246,369144,315080,155560,612264,492069,844778,

%U 1414099,871855,436812,959459,490218,1232476,5122720,1649231,2961709

%N Sum of primes between successive squares of primes.

%F a(n) = sum of primes between (prime(n))^2 and (prime(n+1))^2.

%e a(1)=12 because between (prime(1))^2=2^2=4 and (prime(2))^2=3^2=9 there are 2 primes {5,7} which sum to 12

%e a(2)=83 because between (prime(2))^2=9 and (prime(3))^2=25 there are 5 primes {11,13,17,19,23} which sum to 83

%e a(3)=228 because between 5^2=25 and 7^2=49 there are 6 primes {29,31,37,41,43,47} which sum to 228

%e a(4)=1265 because between 49 and 121 there are 15 primes {53..113} which sum to 1265

%e a(5)=1321 because between 121 and 169 there are 9 primes {127..167} which sum to 1321.

%t Table[Total[Select[Range[Prime[n]^2,Prime[n+1]^2],PrimeQ]],{n,60}]

%t Total[Select[Range[#[[1]],#[[2]]],PrimeQ]]&/@ Partition[Prime[ Range[ 40]]^2,2,1] (* _Harvey P. Dale_, Jul 13 2015 *)

%Y Cf. A050216 (number of primes between (prime(n))^2 and (prime(n+1))^2).

%K nonn

%O 1,1

%A _Zak Seidov_, Nov 12 2009