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A277186
Sum of primes within 2n-wide closed interval centered upon prime(n).
0
5, 10, 17, 26, 31, 67, 83, 83, 119, 139, 161, 228, 281, 281, 341, 408, 474, 553, 546, 635, 635, 780, 824, 1092, 954, 1008, 1008, 1139, 1197, 1336, 1621, 1687, 1650, 1823, 1854, 1854, 2238, 2634, 2507, 2587, 2450, 2673, 3223, 3223, 3403, 3403, 3591, 4054, 4054, 4331, 4535, 4535, 4828, 4444, 4666
OFFSET
1,1
COMMENTS
a(n) is the sum of primes within the closed interval [prime(n)-n, prime(n)+n], where prime(n) is the n-th prime.
EXAMPLE
a(3) = 2 + 3 + 5 + 7 = 17; starting at prime(3) = 5, subtract 3 and add 3 to obtain the interval 2 through 8, and then add up the primes within that interval, inclusive of the endpoints of the interval.
MATHEMATICA
Table[Total@ Select[Range[Prime@ n - n, Prime@ n + n], PrimeQ], {n, 55}] (* Michael De Vlieger, Oct 04 2016 *)
PROG
(PARI) a(n) = sum(k=prime(n)-n, prime(n)+n, isprime(k)*k); \\ Michel Marcus, Nov 01 2016
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Walter Carlini, Oct 04 2016
EXTENSIONS
More terms from Michael De Vlieger, Oct 04 2016
STATUS
approved