Search: id:A014688
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%I A014688
%S A014688 3,5,8,11,16,19,24,27,32,39,42,49,54,57,62,69,76,79,86,91,94,101,106,
%T A014688 113,122,127,130,135,138,143,158,163,170,173,184,187,194,201,206,213,
%U A014688 220,223,234,237,242,245,258,271,276,279,284,291,294,305,312,319,326
%N A014688 a(n) = n-th prime + n.
%C A014688 Conjecture: this sequence contains an infinite number of primes (A061068), 
               yet contains arbitrarily long "prime deserts" such as the 11 composites 
               in A014688 between a(6) = 19 and a(18) = 79 and the 17 composites 
               in A014688 between a(48) = 271 and a(66) = 383. - Jonathan Vos Post 
               (jvospost3(AT)gmail.com), Nov 22 2004
%C A014688 May be obtained by a sieve on the sequence of natural numbers. Starting 
               from n=1 delete the number corresponding to the alternate sum of 
               the preceding left numbers. Iterate with the successive left number. 
               First step n=1, k=1-0=1: delete the k.th number after n ->2. Move 
               to successive remaining number n=3. Then k=3-1+0=2: delete the k.th 
               number after n -> 5. Move to successive remaining number n=4. Then 
               k=4-3+1-0=2. After 4 we have 6,7,8... (5 deleted in previous step). 
               So delete n=7. And so on. - Paolo P. Lava & Giorgio Balzarotti (ppl(AT)spl.at), 
               Jul 14 2008
%C A014688 a(n) = n + A000040(n) = n + A008578(n+1) = n + A158611(n+2). [From Jaroslav 
               Krizek (jaroslav.krizek(AT)atlas.cz), Aug 31 2009]
%C A014688 Complement of A064427. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), 
               Oct 28 2009]
%F A014688 a(n) = A090178(n+1) - 1 = (n+1)-th noncomposite number + n for n >= 2. 
               a(n) = A167136(n+1). a(1) = 3, a(n) = a(n-1) + A008578(n+1) - A008578(n) 
               + 1 for n >= 2. a(1) = 3, a(n) = a(n-1) + A001223(n-1) + 1 for n 
               >= 3. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Oct 28 
               2009]
%p A014688 P:=proc(i) local a,n; for n from 1 by 1 to i do a:=ithprime(n)+n; print(a); 
               od; end: P(100); - Paolo P. Lava (ppl(AT)spl.at), Jul 14 2008
%Y A014688 Cf. A000040, A093570, A093571, A076556, A061068.
%Y A014688 Sequence in context: A159325 A049706 A080415 this_sequence A167136 A099836 
               A136684
%Y A014688 Adjacent sequences: A014685 A014686 A014687 this_sequence A014689 A014690 
               A014691
%K A014688 nonn,easy
%O A014688 1,1
%A A014688 Mohammad K. Azarian (ma3(AT)evansville.edu)
%E A014688 More terms from Vasiliy Danilov (danilovv(AT)usa.net) 1998 Jul
%E A014688 Corrected for changes of offsets of A008578 and A158611 Jaroslav Krizek 
               (jaroslav.krizek(AT)atlas.cz), Oct 28 2009

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