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

1,1

Links

Table of n, a(n) for n=1..32.

Formula

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

Example

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.

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 *)

Crossrefs

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

Sequence in context: A164300 A239180 A290715 * A252179 A102105 A275743

Adjacent sequences: A175034 A175035 A175036 * A175038 A175039 A175040

Keyword

nonn

Author

Zak Seidov, Nov 12 2009

Status

approved