A174550 Run lengths of 2 or larger for consecutive prime numbers in A006577.

3, 2, 2, 2, 2, 2, 4, 2, 3, 3, 2, 2, 3, 3, 4, 2, 5, 4, 3, 2, 3, 4, 2, 2, 2, 2, 3, 3, 2, 5, 2, 2, 3, 2, 3, 2, 2, 3, 8, 2, 4, 2, 2, 2, 2, 2, 3, 3, 3, 6, 3, 4, 2, 2, 3, 3, 2, 2, 4, 2, 2, 3, 6, 2, 3, 2, 2, 2, 5, 2, 2, 2, 2, 2, 2, 2, 5, 3, 2, 4, 3, 5, 3, 3, 2, 8, 2, 2, 2, 2, 3, 8, 4, 3, 3, 3, 4, 2, 3, 8, 2, 3, 3, 5, 3

Offset

1,1

Comments

This sequence is given only for n <=5000 with max(s(n)) = 10. But we can find long sequences of primes, for example,length(s(12956))= 55, and corresponding to A006577(282984 + k), k = 0,1,...,54. We obtain a sequence of 55 consecutive primes numbers given in the example below.

Links

Table of n, a(n) for n=1..105.

Example

a(1) = 3 represents the run (7, 2, 5).
a(2) = 2 represents the run (3, 19).
a(3)=2 represents the run (17, 17).
a(7) = 4 represents the run (19, 19, 107, 107).
a(12956) = 55 represents the run (83, 251, 83, 251, 127, 127, 127, 251, 83, 83, 83, 83, 83, 83, 83, 83, 83, 251, 83, 83, 83, 83, 83, 83, 101, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 251, 251, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83, 83)

Maple

 nn:=2000:T:=array(1..nn):for n from 1 to nn do: m:=n:for p from 0 to 1000 while (m<>1) do: if irem(m, 2)=1 then m:=3*m+1:else m:=m/2:fi:od:T[n]:=p:od:ii:=1:for i from 1 to nn do:if type(T[i], prime)=true and type(T[i+1], prime)=true then ii:=ii+1:else if ii<>1 then printf(`%d, `, ii):ii:=1:else fi:fi:od:

Crossrefs

Cf. A174538, A006577, A066906.

Sequence in context: A270003 A067438 A178250 * A119704 A104223 A057934

Adjacent sequences: A174547 A174548 A174549 * A174551 A174552 A174553

Keyword

nonn,less

Author

Michel Lagneau, Mar 22 2010

Status

approved