1,1

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

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

a(n) = n + A000040(n) = n + A008578(n+1) = n + A158611(n+2). [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Aug 31 2009]

Complement of A064427. [From Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Oct 28 2009]

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:=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

Cf. A000040, A093570, A093571, A076556, A061068.

Sequence in context: A159325 A049706 A080415 this_sequence A167136 A099836 A136684

Adjacent sequences: A014685 A014686 A014687 this_sequence A014689 A014690 A014691

nonn,easy,new

Mohammad K. Azarian (ma3(AT)evansville.edu)

More terms from Vasiliy Danilov (danilovv(AT)usa.net) 1998 Jul

Corrected for changes of offsets of A008578 and A158611 Jaroslav Krizek (jaroslav.krizek(AT)atlas.cz), Oct 28 2009