A277186 Sum of primes within 2n-wide closed interval centered upon prime(n).

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

Author

Walter Carlini, Oct 04 2016

Keywords

• nonn
• easy

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.

Examples

			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.
		

Crossrefs

Cf. A000040, A014688, A014689, A061397.

Programs

Mathematica

Table[Total@ Select[Range[Prime@ n - n, Prime@ n + n], PrimeQ], {n, 55}] (* Michael De Vlieger, Oct 04 2016 *)

PARI

a(n) = sum(k=prime(n)-n, prime(n)+n, isprime(k)*k); \\ Michel Marcus, Nov 01 2016

Extensions

More terms from Michael De Vlieger, Oct 04 2016