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

1,1

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

Example

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

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 *)

Prog

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

Crossrefs

See A051610 and A116111 for records. Cf. A025017.

Cf. A010051, A000040.

Sequence in context: A028401 A005655 A277063 * A051610 A322851 A230950

Adjacent sequences: A051166 A051167 A051168 * A051170 A051171 A051172

Keyword

nice,nonn

Author

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

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

Status

approved