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A001751
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Primes together with primes multiplied by 2.
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18
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2, 3, 4, 5, 6, 7, 10, 11, 13, 14, 17, 19, 22, 23, 26, 29, 31, 34, 37, 38, 41, 43, 46, 47, 53, 58, 59, 61, 62, 67, 71, 73, 74, 79, 82, 83, 86, 89, 94, 97, 101, 103, 106, 107, 109, 113, 118, 122, 127, 131, 134, 137, 139, 142, 146, 149, 151, 157, 158, 163, 166
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OFFSET
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1,1
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COMMENTS
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For n > 1, a(n) is position of primes in A026741.
For n > 1, a(n) is the position of the ones in A046079. - Ant King, Jan 29 2011
A251561(a(n)) != a(n). - Reinhard Zumkeller, Dec 27 2014
Number of terms <= n is pi(n) + pi(n/2). - Robert G. Wilson v, Aug 04 2017
Number of terms <=10^k: 7, 40, 263, 1898, 14725, 120036, 1013092, 8762589, 77203401, 690006734, 6237709391, 56916048160, 523357198488, 4843865515369, ..., . - Robert G. Wilson v, Aug 04 2017
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LINKS
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T. D. Noe, Table of n, a(n) for n = 1..10000
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MATHEMATICA
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Select[Range[163], Or[PrimeQ[#], PrimeQ[1/2 #]] &] (* Ant King, Jan 29 2011 *)
upto=200; With[{pr=Prime[Range[PrimePi[upto]]]}, Select[Sort[Join[pr, 2pr]], # <= upto&]] (* Harvey P. Dale, Sep 23 2014 *)
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PROG
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(Haskell)
a001751 n = a001751_list !! (n-1)
a001751_list = 2 : filter (\n -> (a010051 $ div n $ gcd 2 n) == 1) [1..]
-- Reinhard Zumkeller, Jun 20 2011 (corrected, improved), Dec 17 2010
(PARI) isA001751(n)=isprime(n/gcd(n, 2)) || n==2
(PARI) list(lim)=vecsort(concat(primes(primepi(lim)), 2* primes(primepi(lim\2)))) \\ Charles R Greathouse IV, Oct 31 2012
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CROSSREFS
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Union of A001747 and A000040.
Subsequence of A039698 and of A033948.
Cf. A026741, A046079, A178156, A251561.
Sequence in context: A205666 A245809 A064295 * A191927 A116000 A251595
Adjacent sequences: A001748 A001749 A001750 * A001752 A001753 A001754
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane
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STATUS
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approved
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