A108314 Sum of primes p with n^2 < p < (n+1)^2.

5, 12, 24, 59, 60, 168, 173, 290, 269, 533, 534, 787, 917, 830, 1420, 1901, 1541, 2076, 2288, 2953, 3219, 3533, 3348, 5413, 5208, 4907, 6026, 7343, 6960, 7444, 9948, 9483, 11166, 10749, 12624, 11903, 12713, 17724, 17155, 19590, 18975, 16249, 22702, 21859, 26943

Offset: 1

Author

Giovanni Teofilatto, Jun 30 2005

Keywords

• easy
• nonn

Examples

			a(2)=12 because between 4 and 9 there are two primes (5 and 7) with sum equal to 12.
		

Links

• Michael S. Branicky, Table of n, a(n) for n = 1..10000 (terms 1..1000 from T. D. Noe)

Crossrefs

Cf. A014085, A158528, A293697.

Programs

Maple

a:=proc(n) local s,j: s:=0: for j from n^2 to (n+1)^2 do if isprime(j)=true then s:=s+j else s:=s: fi od end: seq(a(n),n=1..50); # Emeric Deutsch, Jul 01 2005

Mathematica

f[n_] := Plus @@ Prime[ Range[PrimePi[n^2] + 1, PrimePi[(n + 1)^2]]]; Table[ f[n], {n, 44}] (* Robert G. Wilson v, Jul 01 2005 *)

PARI

A108314(n)={r=0;forprime(i=n^2+1,(n+1)^2-1,r=r+i);r} \\ Michael B. Porter, Oct 14 2009

Python

from sympy import sieve
def a(n): return sum(p for p in sieve.primerange(n**2, (n+1)**2))
print([a(n) for n in range(1, 46)]) # Michael S. Branicky, Jul 29 2021

Extensions

Edited, corrected and extended by Emeric Deutsch, Robert G. Wilson v and Rick L. Shepherd, Jul 01 2005