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%I #4 Jul 12 2015 15:59:07
%S 1,2,3,5,6,8,10,12,14,15,17,19,21,23,25,27,29,31,33,35,37,39,41,42,44,
%T 46,48,50,52,54,56,58,60,62,64,66,68,70,72,74,76,78,80,82,84,86,88,90,
%U 92,94,96,98,100,102,104,106,108,110,112,114,116,118,120,122,123,125
%N Variation on Connell sequence (A001614). In this one, a(1)=1, terms a(n) onwards are generated in "blocks" as the next a(n-1) odd numbers > a(n-1) if the previous block ends with a(n-1) even and the next a(n-1) even numbers > a(n-1) if the previous block ends with a(n-1) odd.
%C The entries at the end of each odd or even block are 1,2,5,14,41,122,363,... and the first differences of these are 1,3,9,27,81,241=powers of 3.
%F a(n) = round( LambertW(3^((4*n-3)/2)*log(3)/2)/log(3)) = round( LambertW(x*exp((4*n-3)*x))/(2*x) ), where x=log(sqrt(3)). - Antonio G. Astudillo (afg_astudillo(AT)hotmail.com), Feb 13 2003
%e a(4)=5, which is odd, so the next terms from a(5) onwards are the next 5 even numbers greater than 5: 6,8,10,12,14. Thus the term 14 is followed by the next 14 odd numbers: 15,17,...,41 and so on.
%Y Cf. A001614.
%K nonn
%O 1,2
%A Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 12 2003
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