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

3, 6, 15, 49, 49, 49, 49, 110, 154, 154, 278, 278, 278, 278, 496, 496, 496, 496, 496, 496, 1321, 1321, 1321, 1321, 1321, 1321, 2686, 2686, 2686, 2686, 2686, 2686, 2686, 3713, 3713, 3713, 3713, 3713, 3713, 21766, 21766, 21766, 21766, 21766, 21766, 21766

Offset: 1

Author

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

Keywords

• nice
• nonn

Examples

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

References

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

Links

• Paul S. Bruckman and T. D. Noe, Table of n, a(n) for n = 1..974

Crossrefs

See A051610 and A116111 for records. Cf. A025017.

Cf. A010051, A000040.

Programs

Haskell

a051169 n = head [m | m <- [2..],
            all (== 0) $ map (a010051' . (2*m -)) $ take n a000040_list]
-- Reinhard Zumkeller, Apr 09 2015

Mathematica

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-François Alcover, Jul 17 2012 *)
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 *)

Extensions

More terms from Paul S. Bruckman, Jan 20 2007

Edited by N. J. A. Sloane, Apr 14 2007, May 04 2007, Jun 10 2008