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%I A254897 #14 Mar 29 2015 23:07:00
%S A254897 2,19,31,59,83,107,113,149,157,181,197,229,241,263,271,307,313,331,
%T A254897 353,367,379,389,409,431,439,457,487,499,541,569,577,593,601,617,647,
%U A254897 661,719,733,751,809,823,853,859,877,883,911,937,953,977,997,1019
%N A254897 Define a family of sequences as follows: a(1) and a(2) are prime numbers, then if a(n-2) and a(n-1) have the same parity a(n)=(a(n-2)+a(n-1))/2 and if not a(n)=a(n-2)/2+a(n-1) for a(n-2) even or a(n)=a(n-2)+a(n-1)/2 for a(n-1) even. Start the first sequence with the two smallest prime numbers 2 and 3; in general, start the next sequence with the two smallest prime numbers not present in all preceding sequences; the present sequence lists the initial term of all these sequences.
%H A254897 Pierre CAMI, <a href="/A254897/b254897.txt">Table of n, a(n) for n = 1..10000</a>
%e A254897 a(1)=2, the first term of the sequence A254498.
%e A254897 a(2)=19, the first term of the sequence A254330.
%e A254897 a(3)=31, the smallest prime number not present in A254498 and A254330, and the next one is 37, 31 and 37 starts the third sequence define by the rule, and so on.
%Y A254897 Cf. A254498, A254330.
%K A254897 nonn
%O A254897 1,1
%A A254897 _Pierre CAMI_, Feb 10 2015

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