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A077914 Numbers which can be expressed as the sum of two distinct primes in exactly two ways. 4
16, 18, 20, 22, 26, 28, 32, 62, 68, 9974, 10000, 10004, 10144, 10148, 10154, 10172, 10186, 10214, 10216, 10222, 10238, 10244, 10258, 10268, 10274, 10280, 10292, 10298, 10302, 10304, 10316, 10326, 10328, 10330, 10334, 10336, 10340, 10342, 10362, 10376, 10378 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

COMMENTS

Most likely no more terms. See A117929. - T. D. Noe, Mar 21 2012

LINKS

Table of n, a(n) for n=1..41.

G. L. Honaker, Jr., Prime Curio for 16, April 2000.

EXAMPLE

22 is a term as 22 = 19+3 = 17+5 are the only two ways to express 22 as a sum of two distinct primes.

MAPLE

P:=proc(q, w) local a, k, n;

for n from 1 to q do a:=0; for k from 1 to trunc(n/2) do

if isprime(k) and isprime(n-k) and n<>2*k then a:=a+1; fi; od;

if a=w then print(n); fi; od; end: P(100, 2); # Paolo P. Lava, May 21 2014

MATHEMATICA

Module[{nn=700, max}, max=Prime[nn]+Prime[nn-1]; Select[Union[Select[ Tally[ Total/@Subsets[Prime[Range[nn]], {2}]], #[[2]]==2&][[All, 1]]], #<(max+1)&]] (* Harvey P. Dale, Dec 11 2018 *)

CROSSREFS

Cf. A077969 (3 ways), A078299 (4 ways), A080854 (5 ways), A080862 (6 ways).

Sequence in context: A043705 A178980 A031315 * A273543 A274127 A161874

Adjacent sequences:  A077911 A077912 A077913 * A077915 A077916 A077917

KEYWORD

nonn

AUTHOR

Shyam Sunder Gupta, Mar 29 2003

EXTENSIONS

More terms from Harvey P. Dale, Dec 11 2018

STATUS

approved

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Last modified September 16 10:23 EDT 2019. Contains 327094 sequences. (Running on oeis4.)