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Smallest number m greater than n such that the happy couples of m and n have a member in common.
2

%I #4 Mar 30 2012 18:51:10

%S 2,3,5,6,7,8,10,12,12,11,13,15,17,18,20,20,19,22,23,24,28,32,26,28,30,

%T 27,29,35,31,35,37,34,39,38,42,42,41,40,52,46,43,48,47,52,55,54,50,56,

%U 56,51,53,60,58,62,70,63,69,59,61,68,65,66,72,72,67,86

%N Smallest number m greater than n such that the happy couples of m and n have a member in common.

%C The intersection of {A007966(n),A007967(n)} and {A007966(a(n)),A007967(a(n))} is not empty, but the intersection of {A007966(n),A007967(n)} and {A007966(m),A007967(m)} is empty for n<m<a(n).

%H J. H. Conway, <a href="http://www.cs.uwaterloo.ca/journals/JIS/happy.html">On Happy Factorizations</a>, J. Integer Sequences, Vol. 1, 1998, #1.

%e Let hc(n) = (A007966(n),A007967(n)),

%e n=6, a(6) = 8: hc(6) = (2,3) and hc(8) = (2,4) with common 2,

%e n=7, a(7) = 10: hc(7) = (7,1) and hc(10) = (1,10) with common 1,

%e n=8, a(8) = 12: hc(8) = (2,4) and hc(12) = (3,4) with common 4,

%e n=9, a(9) = 12: hc(9) = (3,3) and hc(12) = (3,4) with common 3.

%K nonn

%O 1,1

%A _Reinhard Zumkeller_, Jun 19 2011