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A051169 Smallest number m such that 2*m - p is composite for the first n primes p. 3

%I

%S 3,6,15,49,49,49,49,110,154,154,278,278,278,278,496,496,496,496,496,

%T 496,1321,1321,1321,1321,1321,1321,2686,2686,2686,2686,2686,2686,2686,

%U 3713,3713,3713,3713,3713,3713,21766,21766,21766,21766,21766,21766,21766

%N Smallest number m such that 2*m - p is composite for the first n primes p.

%D Computed by Peter G. Anderson at the Rochester Institute of Technology.

%H Paul S. Bruckman and T. D. Noe, <a href="/A051169/b051169.txt">Table of n, a(n) for n=1..974</a>

%e a(2) = 6 because 2*6-2 = 10 and 2*6-3 = 9 are composite.

%t a[n_] := a[n] = Catch[For[m = 2, True, m++, If[And @@ (! PrimeQ[2*m - #] &) /@ Prime /@ Range[n], Throw[m]]]]; Table[ Print[a[n]]; a[n], {n, 1, 46}] (* _Jean-Fran├žois Alcover_, Jul 17 2012 *)

%t Module[{nn=50,prs},prs=Prime[Range[nn]];Table[SelectFirst[Range[50000], AllTrue[Table[2#-p,{p,Take[prs,n]}],CompositeQ]&],{n,nn}]] (* The program uses the AllTrue function from Mathematica version 10 *) (* _Harvey P. Dale_, Mar 18 2015 *)

%o (Haskell)

%o a051169 n = head [m | m <- [2..],

%o all (== 0) $ map (a010051' . (2*m -)) $ take n a000040_list]

%o -- _Reinhard Zumkeller_, Apr 09 2015

%Y See A051610 and A116111 for records. Cf. A025017.

%Y Cf. A010051, A000040.

%K nice,nonn

%O 1,1

%A Paul S. Bruckman (pbruckman(AT)hotmail.com)

%E More terms from Paul S. Bruckman, Jan 20 2007

%E Edited by _N. J. A. Sloane_, Apr 14 2007, May 04 2007, Jun 10 2008

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Last modified February 19 22:38 EST 2019. Contains 320328 sequences. (Running on oeis4.)