A080612 Numbers n such that 1/p(2n+1)*sum(k=1,n,p(2k+1)-p(2k)) >= 1/p(2*n)*sum(k=1,n,p(2k)-p(2k-1)) where p(k) denotes the k-th prime.

1, 2, 3, 4, 5, 7, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40, 41, 42, 43, 44, 45, 46, 47, 48, 49, 50, 51, 52, 53, 54, 55, 56, 57, 58, 59, 60, 61, 62, 63, 64, 65, 66, 67, 68, 69, 70, 71, 72, 73, 74

Offset

1,2

Comments

Conjectured to be finite with last term = 314. Other conjecture log(n)^2*(1/p(2n+1)*sum(k=1,n,p(2k+1)-p(2k)) - 1/p(2*n)*sum(k=1,n,p(2k)-p(2k-1))) -> constant. Weaker : previous formula is bounded.

Links

Table of n, a(n) for n=1..72.

Crossrefs

Sequence in context: A115928 A247665 A117331 * A039261 A039201 A039151

Adjacent sequences: A080609 A080610 A080611 * A080613 A080614 A080615

Keyword

nonn

Author

Benoit Cloitre, Feb 25 2003

Status

approved