1,1

Comment from Vladimir Shablayev (shevelev(AT)bgu.ac.il): Conjecture: a(n) < A027699(n) except for n = 2. I verified this conjecture up to n=5*10^7. Moreover, I conjecture that A027699(n) - a(n) tends to infinity.

Item 2 of Green is about this sequence: "This is an expository article to accompany my two lectures at the CDM conference. I have used this an excuse to make public two sets of notes I had lying around, and also to put together a short reader's guide to some recent joint work with T. Tao. Contents: 1. An exposition, without much detail, of the work of Goldston, Pintz and Yildirim on gaps between primes; 2. A detailed discussion of the work of Mauduit and Rivat establishing that 50 percent of the primes have odd digit sum when written in base 2; 3. A reader's guide to recent work of T. Tao and the author on linear equations in primes. The sections can be read independently." - Jonathan Vos Post (jvospost2(AT)yahoo.com), Oct 04 2007

T. D. Noe, Table of n, a(n) for n=1..10000

Ben Green, Three topics in additive prime number theory, Oct 03, 2007, pp. 12-27.

a:=proc(n) local nn: nn:= convert(ithprime(n), base, 2): if `mod`(sum(nn[j], j =1..nops(nn)), 2)=1 then ithprime(n) else end if end proc: seq(a(n), n=1..103); - Emeric Deutsch (deutsch(AT)duke.poly.edu), Oct 24 2007

Cf. A027699, A066148, A066149.

Cf. A000069 (odious numbers), A092246 (odd odious numbers)

Sequence in context: A097143 A038897 A020583 this_sequence A038892 A019346 A045369

Adjacent sequences: A027694 A027695 A027696 this_sequence A027698 A027699 A027700

nonn,easy,base

njas

More terms from Scott Lindhurst (ScottL(AT)alumni.princeton.edu)