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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.

Index entries for sequences related to Goldbach conjecture

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-Fran├žois 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

N. J. A. Sloane.

STATUS

approved

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