

A175037


Sum of primes between successive squares of primes.


1



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
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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



