

A161782


a(n) = sum of all numbers from and including (prime(n+1)prime(n)) to and including (prime(n+2)prime(n).)


1



6, 9, 20, 15, 20, 15, 20, 49, 21, 35, 40, 15, 20, 49, 63, 21, 35, 40, 15, 35, 40, 49, 90, 50, 15, 20, 15, 20, 165, 80, 49, 21, 77, 33, 35, 63, 40, 49, 63, 21, 77, 33, 20, 15, 104, 234, 70, 15, 20, 49, 21, 77, 91, 63, 63, 21, 35, 40, 15, 77, 255, 80, 15, 20, 165, 119, 121, 33
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OFFSET

1,1


LINKS



FORMULA

a(n) = Sum_{x=prime(n+1)prime(n)..prime(n+2)prime(n)} x = Sum_{x=A001223(n)..A031131(n)} x.


EXAMPLE

n = 1: prime(1) = 2, prime(2) = 3, prime(3) = 5. Sum of all numbers from prime(2)prime(1) = 1 to prime(3)prime(1) = 3 is 1+2+3, hence a(1) = 6.
n = 11: prime(11) = 31, prime(12) = 37, prime(13) = 41. Sum of all numbers from prime(12)prime(11) = 6 to prime(13)prime(11) = 10 is 6+7+8+9+10, hence a(11) = 40.


MATHEMATICA

Total[Range[#[[2]]#[[1]], #[[3]]#[[1]]]]&/@Partition[Prime[Range[70]], 3, 1] (* Harvey P. Dale, Oct 18 2021 *)


PROG

MAGMA) [ &+[(NthPrime(n+1)NthPrime(n))..(NthPrime(n+2)NthPrime(n))]: n in [1..68] ];


CROSSREFS

Cf. A001223 (differences between consecutive primes), A031131 (difference between nth prime and (n+2)nd prime).


KEYWORD

nonn


AUTHOR



EXTENSIONS



STATUS

approved



