A161180 Sum of primes between n^2 and n^2+n, n^2+n and (n+1)^2. The only intervals for which n^2+n is prime are [1,2], [2,4] and the endpoint 2 is included in the sum. One might have written 0,3,5,7,..., etc.

2, 5, 5, 7, 11, 13, 36, 23, 29, 31, 78, 90, 53, 120, 138, 152, 172, 97, 420, 113, 258, 276, 300, 487, 533, 384, 396, 434, 928, 492, 1060, 841, 293, 1248, 668, 1408, 1119, 1169, 1229, 1724, 1810, 1409, 1980, 1553, 1088, 2260, 2356, 3057, 2562, 2646, 2752, 2155

Offset

1,1

Links

Table of n, a(n) for n=1..52.

Example

On [1,2] the sum of primes is 2. For [2,4] the sum is 5. [4,6]: 5, [6,9]: 7, [9,12]: 11, [12,16]: 13, [16,20]: 17+19 = 36.

Maple

A161180 := proc(n) a := 0 ; if type(n, 'odd') then nloc := (n+1)/2 ; for p from nloc^2 to nloc^2+nloc do if isprime(p) then a := a+p ; end if; end do: else nloc := n/2 ; for p from nloc^2+nloc to (nloc+1)^2 do if isprime(p) then a := a+p ; end if; end do: end if; a; end proc: seq(A161180(n), n=1..120) ; # R. J. Mathar, May 31 2010

Crossrefs

Cf. A160907

Sequence in context: A175649 A240497 A142353 * A101858 A329813 A165917

Adjacent sequences: A161177 A161178 A161179 * A161181 A161182 A161183

Keyword

easy,nonn

Author

Daniel Tisdale, Jun 05 2009

Extensions

Corrected (128 replaced by 138) and extended by R. J. Mathar, May 31 2010

Status

approved