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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 (list; graph; refs; listen; history; text; internal format)
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.

LINKS

Table of n, a(n) for n=1..42.

Abelard, On Computable Numbers, with an Application to the Entscheidungsproblem, By A. M. Turing

Michael S. Branicky, Python TM Simulation Code

S. Britton, Turing Machine Simulator [Dead link]

M. Ugarte, Turing Machine Simulator

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

Adjacent sequences:  A078609 A078610 A078611 * A078613 A078614 A078615

KEYWORD

nonn

AUTHOR

Jason Earls, Dec 10 2002

EXTENSIONS

Terms beyond a(9) from Michael S. Branicky, Jul 04 2020

STATUS

approved

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Last modified August 1 17:41 EDT 2021. Contains 346402 sequences. (Running on oeis4.)