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 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
KEYWORD
nonn
AUTHOR
EXTENSIONS
More terms from Robert G. Wilson v, Aug 31 2008
STATUS
approved