%I #16 Jun 16 2023 18:45:06

%S 17,65,89,127,137,163,179,185,191,233,247,269,305,343,427,457,547,569,

%T 583,613,637,667,673,697,733,757,779,787,817,821,853,929,967,977,989,

%U 997,1045,1087,1117,1207,1267,1273,1289,1297,1327,1345,1357

%N Numbers in A014092 splittable into a sum of a single number pair (both distinct from 1) having a product that belongs to A086473.

%C The first term is the sum solution of Martin Gardner's "Impossible Problem" for numbers each with an upper bound anywhere between 62 and 100.

%D M. Gardner,"Mathematical Games" Problem 1 pp. 20, 23-24 in Scientific American, Dec. 1979.

%H G. Darby, <a href="http://www.delphiforfun.org/Programs/know_dont_know.htm">Know, Don't Know Problem</a>.

%H R. V. Gassel et al., <a href="http://puzzle.dse.nl/logical/index_us.html#know_or_not">To Know, or Not To Know</a>.

%H K. Uhland, <a href="https://web.archive.org/web/20041115232552/http://uhlandkf.homestead.com:80/files/PuzzlePage/199812Pzl.htm">A Great Puzzle</a>.

%Y For the corresponding (unique) products see A086860.

%Y The number pairs are given by {a(n) -+ A086888(n)}/2.

%Y Cf. A014092, A086473.

%K nonn

%O 1,1

%A _Lekraj Beedassy_, Sep 10 2003