A175037 Sum of primes between successive squares of primes.

12, 83, 228, 1265, 1321, 5068, 3617, 11993, 32245, 14404, 65873, 67182, 35224, 93088, 201244, 245920, 115246, 369144, 315080, 155560, 612264, 492069, 844778, 1414099, 871855, 436812, 959459, 490218, 1232476, 5122720, 1649231, 2961709

Offset: 1

Author

Zak Seidov, Nov 12 2009

Keywords

• nonn

Examples

			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
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
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
a(4)=1265 because between 49 and 121 there are 15 primes {53..113} which sum to 1265
a(5)=1321 because between 121 and 169 there are 9 primes {127..167} which sum to 1321.
		

Crossrefs

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

Programs

Mathematica

Table[Total[Select[Range[Prime[n]^2,Prime[n+1]^2],PrimeQ]],{n,60}]
Total[Select[Range[#[[1]],#[[2]]],PrimeQ]]&/@ Partition[Prime[ Range[ 40]]^2,2,1] (* Harvey P. Dale, Jul 13 2015 *)

Formula

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