%I #40 Oct 17 2024 12:52:16
%S 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,
%T 58,59,61,62,67,71,73,74,79,82,83,86,89,94,97,101,103,106,107,109,113,
%U 118,122,127,131,134,137,139,142,146,149,151,157,158,163,166
%N Primes together with primes multiplied by 2.
%C For n > 1, a(n) is position of primes in A026741.
%C For n > 1, a(n) is the position of the ones in A046079. - _Ant King_, Jan 29 2011
%C A251561(a(n)) != a(n). - _Reinhard Zumkeller_, Dec 27 2014
%C Number of terms <= n is pi(n) + pi(n/2). - _Robert G. Wilson v_, Aug 04 2017
%C 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
%C Complement of A264828. - _Chai Wah Wu_, Oct 17 2024
%H T. D. Noe, <a href="/A001751/b001751.txt">Table of n, a(n) for n = 1..10000</a>
%t Select[Range[163], Or[PrimeQ[#], PrimeQ[1/2 #]] &] (* _Ant King_, Jan 29 2011 *)
%t upto=200;With[{pr=Prime[Range[PrimePi[upto]]]},Select[Sort[Join[pr,2pr]],# <= upto&]] (* _Harvey P. Dale_, Sep 23 2014 *)
%o (Haskell)
%o a001751 n = a001751_list !! (n-1)
%o a001751_list = 2 : filter (\n -> (a010051 $ div n $ gcd 2 n) == 1) [1..]
%o -- _Reinhard Zumkeller_, Jun 20 2011 (corrected, improved), Dec 17 2010
%o (PARI) isA001751(n)=isprime(n/gcd(n,2)) || n==2
%o (PARI) list(lim)=vecsort(concat(primes(primepi(lim)), 2* primes(primepi(lim\2)))) \\ _Charles R Greathouse IV_, Oct 31 2012
%o (Python)
%o from sympy import primepi
%o def A001751(n):
%o def bisection(f,kmin=0,kmax=1):
%o while f(kmax) > kmax: kmax <<= 1
%o while kmax-kmin > 1:
%o kmid = kmax+kmin>>1
%o if f(kmid) <= kmid:
%o kmax = kmid
%o else:
%o kmin = kmid
%o return kmax
%o def f(x): return int(n+x-primepi(x)-primepi(x>>1))
%o return bisection(f,n,n) # _Chai Wah Wu_, Oct 17 2024
%Y Union of A001747 and A000040.
%Y Subsequence of A039698 and of A033948.
%Y Cf. A026741, A046079, A178156, A251561, A264828.
%K nonn,easy
%O 1,1
%A _N. J. A. Sloane_