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A014091 Numbers that are the sum of 2 primes. 21
4, 5, 6, 7, 8, 9, 10, 12, 13, 14, 15, 16, 18, 19, 20, 21, 22, 24, 25, 26, 28, 30, 31, 32, 33, 34, 36, 38, 39, 40, 42, 43, 44, 45, 46, 48, 49, 50, 52, 54, 55, 56, 58, 60, 61, 62, 63, 64, 66, 68, 69, 70, 72, 73, 74, 75, 76, 78, 80, 81, 82, 84, 85, 86, 88, 90, 91, 92, 94, 96, 98 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,1
COMMENTS
Sequence consists of all primes + 2 and, conjecturally (Goldbach), of all even integers larger than 2. The Goldbach conjecture is that every even number is the sum of two primes. - Emeric Deutsch, Jul 14 2004
LINKS
David Eisenbud and Brady Haran, Goldbach Conjecture, Numberphile video (2017)
T. Estermann, Proof that every large integer is the sum of two primes and a square, Proc. Lond. Math. Soc. 42 (1937) 501-516.
MAPLE
sort({seq(2+ithprime(j), j=1..21)} union {seq(2*k, k=2..ceil(ithprime(21)/2))}); # Emeric Deutsch, Jul 14 2004
MATHEMATICA
Take[ Union@ Flatten@ Table[ Prime@p + Prime@q, {p, 25}, {q, p}], 71] (* Robert G. Wilson v, Aug 31 2008 *)
PROG
(PARI) isA014091(n)= my(i, p); i=1; p=prime(i); while(p<n, if( isprime(n-p), return(1)); i++; p=prime(i)); 0
n=0; for(a=2, 100, if(isA014091(a), print(n, " ", a); n++)) \\ R. J. Mathar, Aug 20 2006
(PARI) is(n)=if(n%2, isprime(n-2), n>2) \\ on Goldbach's conjecture; Charles R Greathouse IV, Oct 22 2013
(Haskell)
a014091 n = a014091_list !! (n-1)
a014091_list = filter (\x -> any ((== 1) . a010051) $
map (x -) $ takeWhile (< x) a000040_list) [1..]
-- Reinhard Zumkeller, Oct 15 2014
CROSSREFS
Complement = A014092.
Cf. A010051, A000040, A157931 (semiprimes).
Sequence in context: A162706 A088331 A239433 * A308040 A287961 A030791
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Robert G. Wilson v, Aug 31 2008
STATUS
approved

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Last modified July 25 11:18 EDT 2024. Contains 374588 sequences. (Running on oeis4.)