A212530 Difference between the sum of the first n primes s(n) and the nearest square < s(n).

1, 1, 1, 1, 3, 5, 9, 13, 19, 8, 16, 1, 13, 25, 4, 20, 40, 17, 39, 14, 36, 7, 33, 2, 36, 5, 39, 2, 36, 72, 39, 2, 52, 11, 67, 26, 84, 43, 105, 62, 17, 83, 38, 110, 59, 2, 82, 37, 127, 76, 21, 113, 54, 152, 97, 40, 146, 85, 22, 130, 61, 175, 118, 57, 181, 114

Offset

1,5

Comments

Let A007504(n) the sum of the first n primes. It is proved that between the numbers A007504(n) and A007504(n+1) there must be a square integer.

The sum of the first n primes is asymptotically equivalent to (1/2)*log(n)*n^2.

Links

Michel Lagneau, Table of n, a(n) for n = 1..10000

Example

a(5) = 3 because the sum of the 5 primes 2 + 3 + 5 + 7 + 11 = 28, and 28 - 25 = 3.

Maple

with(numtheory): for n from 1 to 100 do:s:=sum(‘ithprime(k)’, ’k’=1..n):x:=s -floor(sqrt(s-1))^2: printf(`%d, `, x):od:

Crossrefs

Cf. A007504.

Sequence in context: A074133 A215909 A078735 * A004132 A207187 A359185

Adjacent sequences: A212527 A212528 A212529 * A212531 A212532 A212533

Keyword

nonn

Author

Michel Lagneau, May 20 2012

Status

approved