OFFSET
1,1
LINKS
Harvey P. Dale, Table of n, a(n) for n = 1..1000
FORMULA
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
KEYWORD
nonn
AUTHOR
Juri-Stepan Gerasimov, Jun 20 2009
EXTENSIONS
Edited and extended beyond a(33) by Klaus Brockhaus, Jun 23 2009
Definition clarified by Harvey P. Dale, Oct 18 2021
STATUS
approved