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 A025583 Composite numbers that are not the sum of 2 primes. 11
 27, 35, 51, 57, 65, 77, 87, 93, 95, 117, 119, 121, 123, 125, 135, 143, 145, 147, 155, 161, 171, 177, 185, 187, 189, 203, 205, 207, 209, 215, 217, 219, 221, 237, 245, 247, 249, 255, 261, 267, 275, 287, 289, 291, 297, 299, 301, 303, 305, 321, 323, 325, 327, 329, 335, 341 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,1 COMMENTS Goldbach conjectured that every integer >5 is the sum of three primes. Numbers n, such that however many of n coins are placed with heads rather than tails showing, either those showing heads or those showing tails can be arranged in a rectangular pattern with multiple rows and columns. (If the Goldbach conjecture for even numbers is false this comment should be restricted to the odd terms of this sequence, as it might otherwise define a variant sequence). - Peter Munn, May 15 2017 LINKS T. D. Noe, Table of n, a(n) for n = 1..10000 Eric Weisstein's World of Mathematics, Prime Partition. FORMULA Conjecture: This is the sequence of odd numbers such that (n mod x) mod 2 != 1, where x is the greatest m<=n such that m,m-1 and m-2 are all composite. Verified for first 10000 terms. - Benedict W. J. Irwin, May 06 2016 MATHEMATICA f[n_] := (p = 0; pn = PrimePi[n]; Do[ If[n == Prime[i] + Prime[k], p = p + 1; If[p > 2, Break[]]], {i, 1, pn}, {k, i, pn}]; p ); Select[Range[2, 400], ! PrimeQ[#] && f[#] == 0 & ] (* Jean-François Alcover, Mar 07 2011 *) upto=350; With[{c=PrimePi[upto]}, Complement[Range[4, upto], Prime[Range[ c]], Union[Total/@Tuples[Prime[Range[c]], {2}]]]] (* Harvey P. Dale, Jul 14 2011 *) PROG (Haskell) a025583 n = a025583_list !! (n-1) a025583_list = filter f a002808_list where    f x = all (== 0) \$ map (a010051 . (x -)) \$ takeWhile (< x) a000040_list -- Reinhard Zumkeller, Oct 15 2014 CROSSREFS Cf. A051034, A001031, A002372, A002374, A071335. Cf. A002808, A000040, A010051. Sequence in context: A032584 A072492 A164376 * A134101 A226191 A098883 Adjacent sequences:  A025580 A025581 A025582 * A025584 A025585 A025586 KEYWORD nonn,nice,easy AUTHOR STATUS approved

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Last modified July 15 20:24 EDT 2019. Contains 325056 sequences. (Running on oeis4.)