

A014091


Numbers that are the sum of 2 primes.


15



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
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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

T. D. Noe, Table of n, a(n) for n = 1..1000
David Eisenbud and Brady Haran, Goldbach Conjecture  Numberphile (2017)
T. Estermann, Proof that every large integer is the sum of two primes and a square, Proc. Lond. Math. Soc. 42 (1937) 501516.


MAPLE

sort({seq(2+ithprime(j), j=1..21)} union {seq(2*k, k=2..ceil(ithprime(21)/2))}); (Deutsch)


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(np), 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(n2), n>2) \\ on Goldbach's conjecture; Charles R Greathouse IV, Oct 22 2013
(Haskell)
a014091 n = a014091_list !! (n1)
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 * A030791 A227763 A039091
Adjacent sequences: A014088 A014089 A014090 * A014092 A014093 A014094


KEYWORD

nonn,changed


AUTHOR

N. J. A. Sloane.


EXTENSIONS

More terms from Robert G. Wilson v, Aug 31 2008


STATUS

approved



