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%I #32 Feb 13 2014 13:16:05
%S 1,2,2,9,7,14,10,17,21,27,32,43,35,32,43,48,50,54,59,78,71,69,48,75,
%T 74,100,80,85,77,115,105,110,102,137,139,147,148,159,156,186,151,144,
%U 156,166,167,148,222,233,209,247,214,219,249,245,226,241,234,267,243,233,256,292,290,269,283
%N Number of iterations needed to reach 1 when computing repeatedly absolute values of differences of the sequence "2, followed by consecutive primes beginning with the n-th prime". a(n)=0 if 1 is never reached.
%C We conjecture that a(n)>0, and that after reaching the first 1, all further iterations begin with 1. This is a generalization of the well known Gilbreath's conjecture. We call the effect, that a "tail" of 1's appears after a time, "lizard's effect for primes" (see seqfan list from Jun 01 2012).
%H Alois P. Heinz and Zak Seidov, <a href="/A212990/b212990.txt">Table of n, a(n) for n = 2..1000</a> (first 500 terms from Alois P. Heinz)
%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/GilbreathsConjecture.html">Gilbreaths Conjecture</a>
%H Wikipedia, <a href="http://en.wikipedia.org/wiki/Gilbreath%27s_conjecture">Gilbreaths Conjecture</a>
%F Conjecture: limsup a(n)/prime(n) = 1.
%e Let n=6, prime(6) = 13. Then we consider the sequences of primes and iterations of absolute values of differences:
%e 2, 13, 17, 19, 23, 29, 31, 37, ...
%e 11, 4, 2, 4, 6, 2, 6, ...
%e 7, 2, 2, 2, 4, 4, ...
%e 5, 0, 0, 2, 0, ...
%e 5, 0, 2, 2, ...
%e 5, 2, 0, ...
%e 3, 2, ...
%e 1, ...
%e Thus the number of the first iteration beginning with 1 is 7, and a(6)=7.
%Y Cf. A036262.
%K nonn
%O 2,2
%A _Vladimir Shevelev_, Jun 01 2012
%E More terms from _Graeme McRae_ and _Peter J. C. Moses_
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