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A014688
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a(n) = n-th prime + n.
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37
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3, 5, 8, 11, 16, 19, 24, 27, 32, 39, 42, 49, 54, 57, 62, 69, 76, 79, 86, 91, 94, 101, 106, 113, 122, 127, 130, 135, 138, 143, 158, 163, 170, 173, 184, 187, 194, 201, 206, 213, 220, 223, 234, 237, 242, 245, 258, 271, 276, 279, 284, 291, 294, 305, 312, 319, 326
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,1
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COMMENTS
| 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 (paoloplava(AT)gmail.com), 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]
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
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FORMULA
| 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]
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MAPLE
| 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 (paoloplava(AT)gmail.com), Jul 14 2008
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PROG
| (Haskell)
a014688 n = a014688_list !! (n-1)
a014688_list = zipWith (+) [1..] a000040_list
-- Reinhard Zumkeller, Sep 16 2011
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CROSSREFS
| Cf. A000040, A093570, A093571, A076556, A061068.
Sequence in context: A080415 A175489 * A167136 A099836 A194803 A180619
Adjacent sequences: A014685 A014686 A014687 * A014689 A014690 A014691
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KEYWORD
| nonn,easy
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AUTHOR
| Mohammad K. Azarian (ma3(AT)evansville.edu)
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EXTENSIONS
| 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
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