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 A118955 Numbers of the form 2^k + prime. 19
 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 17, 18, 19, 20, 21, 23, 24, 25, 27, 29, 30, 31, 32, 33, 34, 35, 37, 38, 39, 41, 42, 43, 44, 45, 47, 48, 49, 51, 53, 54, 55, 57, 59, 60, 61, 62, 63, 65, 66, 67, 68, 69, 71, 72, 73, 74, 75, 77, 79, 80, 81, 83, 84, 85, 87, 89, 90, 91, 93 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS A109925(a(n)) > 0, complement of A118954; The lower density is at least 0.09368 (Pintz) and upper density is at most 0.49095 (Habsieger & Roblot). The density, if it exists, is called Romanov's constant. Romani conjectures that it is around 0.434. - Charles R Greathouse IV, Mar 12 2008 Elsholtz & Schlage-Puchta improve the bound on lower density to 0.107648. Unpublished work by Jie Wu improves this to 0.110114, see Remark 1 in Elsholtz & Schlage-Puchta. - Charles R Greathouse IV, Aug 06 2021 LINKS Charles R Greathouse IV, Table of n, a(n) for n = 1..10000. Christian Elsholtz and Jan-Christoph Schlage-Puchta, On Romanov's constant, Mathematische Zeitschrift, Vol. 288 (2018), pp. 713-724. Laurent Habsieger and Xavier-Francois Roblot, On integers of the form p + 2^k, Acta Arithmetica 122:1 (2006), pp. 45-50. J. Pintz, A note on Romanov's constant, Acta Mathematica Hungarica 112:1-2 (2006), pp. 1-14. F. Romani, Computations concerning primes and powers of two, Calcolo 20 (1983), pp. 319-336. MATHEMATICA Select[Range[100], (For[r=False; k=1, #>k, k*=2, If[PrimeQ[#-k], r=True]]; r)& ] (* Jean-François Alcover, Dec 26 2013, after Charles R Greathouse IV *) PROG (PARI) is(n)=my(k=1); while(n>k, if(isprime(n-k), return(1), k*=2)); 0 \\ Charles R Greathouse IV, Mar 12 2008 (PARI) list(lim)=my(v=List(), t=1); while(t= startvalue return filter(lambda n: any(isprime(n-(1<

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Last modified April 23 19:56 EDT 2024. Contains 371916 sequences. (Running on oeis4.)