A212990 - OEIS

%I #33 Feb 16 2025 08:33:17

%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="https://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,changed

%O 2,2

%A _Vladimir Shevelev_, Jun 01 2012

%E More terms from _Graeme McRae_ and _Peter J. C. Moses_