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A078612
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.
1
22, 38, 80, 140, 302, 410, 668, 824, 1182, 1832, 2086, 2930, 3572, 3920, 4662, 5892, 7262, 7756, 9320, 10442, 11032, 12884, 14202, 16298, 19310, 20912, 21740, 23438, 24314, 26120, 32900, 34986, 38228, 39350, 45152, 46366, 50092, 53960, 56622, 60732, 64982, 66440
OFFSET
1,1
COMMENTS
The Turing machine computing this sequence uses the 5-tuple instruction table:
[State, Character, New State, New Character, Direction]
{1,_ 1,_,>} {1,1 1,1,>} {1,- 1,-,>} {1,= 2,_,<} {2,1 3,=,<}
{2,- H,_,<} {3,1 3,1,<} {3,- 4,-,<} {4,_ 4,_,<} {4,1 1,_,>}
(Suzanne Britton), with the read-write head beginning at canonical position.
FORMULA
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
PROG
(Python) # See Branicky link
CROSSREFS
Cf. A001223.
Sequence in context: A063252 A078540 A057836 * A039373 A043196 A043976
KEYWORD
nonn
AUTHOR
Jason Earls, Dec 10 2002
EXTENSIONS
Terms beyond a(9) from Michael S. Branicky, Jul 04 2020
STATUS
approved