A082749 Difference between the sum of next prime(n) natural numbers and the sum of next n primes.

1, 4, 9, 10, 54, 71, 191, 236, 446, 1025, 1310, 2259, 3245, 3820, 5048, 7321, 10060, 11473, 15328, 18358, 20381, 25672, 30222, 36561, 46367, 53031, 58108, 65444, 70971, 78391, 104184, 116542, 133095, 142728, 169931, 181324, 203429, 226622

Offset

1,2

Comments

Group the natural numbers with prime(n) elements in each group. (1,2),(3,4,5),(6,7,8,9,10),(11,12,13,14,15,16,17),... The sum corresponding the groups is 3,12,40,98,... Group the prime numbers such that the n-th group contains n primes. (2),(3,5),(7,11,13),(17,19,23,29),... The sum corresponding the groups is 2,8,31,88,... The required difference is 1,4,9,10,...

The following sequences (allowing offset of first term) all appear to have the same parity: A034953, triangular numbers with prime indices; A054269, length of period of continued fraction for sqrt(p), p prime; A082749, difference between the sum of next prime(n) natural numbers and the sum of next n primes; A006254, numbers n such that 2n-1 is prime; A067076, 2n+3 is a prime. - Jeremy Gardiner, Sep 10 2004

Links

Table of n, a(n) for n=1..38.

Formula

a(n) = ((A061802(n-1) + 1)*A000040(n))/2 - A007468(n). - Gionata Neri, May 17 2015

Crossrefs

Sequence in context: A197129 A115688 A115710 * A220427 A115675 A115668

Adjacent sequences: A082746 A082747 A082748 * A082750 A082751 A082752

Keyword

nonn

Author

Amarnath Murthy, Apr 17 2003

Extensions

More terms from Ray Chandler, May 13 2003

Status

approved