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A242561 a(0)=0; thereafter, a(n) is n multiplied by the distance of a(n-1) to the nearest prime.

%I A242561 #19 May 22 2014 15:09:14
%S A242561 0,2,0,6,4,5,0,14,8,9,20,11,0,26,42,15,32,17,0,38,20,21,44,23,0,50,78,
%T A242561 27,56,87,60,31,0,66,34,105,72,37,0,78,40,41,0,86,132,45,92,141,96,49,
%U A242561 100,51,104,53,0,110,56,171,116,177
%N A242561 a(0)=0; thereafter, a(n) is n multiplied by the distance of a(n-1) to the nearest prime.
%C A242561 It appears that any starting value a(0) will produce a sequence which merges with this one at some point.
%C A242561 Also, if we create a new sequence, call it b(n), from this one by changing one term, say a(k), then it appears that there exists an index m such that a(n)=b(n) for all n>=m. For example, if we replace a(10) by 1341, which is a number within the prime gap 1327-1361, then this new sequence has b(17)=a(17) and so the two sequences agree after that point. - _J. M. Bergot_, May 21 2014.
%F A242561 a(n+1) = n*A051699(a(n)), starting a(0)=0.
%e A242561 The sequence begins with a(0)=0, so |2-0|=2 and a(1)=1*2=2; find
%e A242561 the next m=|2-2|=0, so a(2)=0*2=0; find the next m=|2-0|=2, so a(3)=3*2=6; find the next m=|7-6|=1, so a(4)=1*4=4.
%K A242561 nonn
%O A242561 0,2
%A A242561 _J. M. Bergot_, May 17 2014
%E A242561 Edited by _N. J. A. Sloane_, May 20 2014