|
%I #32 Jul 01 2021 04:44:43
%S 22,38,80,140,302,410,668,824,1182,1832,2086,2930,3572,3920,4662,5892,
%T 7262,7756,9320,10442,11032,12884,14202,16298,19310,20912,21740,23438,
%U 24314,26120,32900,34986,38228,39350,45152,46366,50092,53960,56622,60732,64982,66440
%N Number of transitions necessary for a Turing machine to compute the differences between consecutive primes (primes written in unary), when using the instruction table below.
%C The Turing machine computing this sequence uses the 5-tuple instruction table:
%C [State, Character, New State, New Character, Direction]
%C {1,_ 1,_,>} {1,1 1,1,>} {1,- 1,-,>} {1,= 2,_,<} {2,1 3,=,<}
%C {2,- H,_,<} {3,1 3,1,<} {3,- 4,-,<} {4,_ 4,_,<} {4,1 1,_,>}
%C (Suzanne Britton), with the read-write head beginning at canonical position.
%H Abelard, <a href="http://www.abelard.org/turpap2/tp2-ie.asp#section-6">On Computable Numbers, with an Application to the Entscheidungsproblem, By A. M. Turing</a>
%H Michael S. Branicky, <a href="/A078612/a078612.txt">Python TM Simulation Code</a>
%H S. Britton, <a href="http://www.igs.net/~tril/tm/tm.html">Turing Machine Simulator</a> [Dead link]
%H M. Ugarte, <a href="https://turingmachinesimulator.com/">Turing Machine Simulator</a>
%F a(n) = prime(n+1)-prime(n)+(2*prime(n)+3)*(prime(n)+1) because when started with input string 1^q - 1^p =, with q >= p, the Turing machine halts with 1^(q-p) on its tape after (q-p)+(2*p+3)*(p+1) steps. - _Michael S. Branicky_, Jul 04 2020
%o (Python) # See Branicky link
%Y Cf. A001223.
%K nonn
%O 1,1
%A _Jason Earls_, Dec 10 2002
%E Terms beyond a(9) from _Michael S. Branicky_, Jul 04 2020
|
