A174538 The smallest k such that the number of steps in the n Collatz sequences starting at k+i, i=0..n-1, is always prime.

3, 3, 3, 60, 246, 560, 560, 560, 4722, 4722, 6032, 6666, 13956, 13956, 13956, 13956, 13956, 13956, 13956, 13956, 13956, 13956, 13956, 13956, 81488, 81488, 81488, 83840, 89535, 89535, 89535, 282880, 282984, 282984, 282984, 282984

Offset

1,1

Comments

Indices of A006577 that start a run of at least n primes.

We find long sequences of primes, for example there are 55 primes starting at index 282984, namely 83, 101, 127, 251,...

Links

Donovan Johnson, Table of n, a(n) for n = 1..619 (terms <= 10^10)

Index entries for sequences related to 3x+1 (or Collatz) problem

Example

A006577(3)=7, A006577(4)=2 and A006577(5)=5 are all prime, so a(1)=a(2)=a(3) =3 mark the start of that run.

Maple

A174538 := proc(n)
        local k, allp;
        for k from 1 do
                allp := true;
                for i from 0 to n-1 do
                        if not isprime(A006577(k+i)) then
                                allp := false;
                                break;
                        end if;
                end do:
                if allp then
                        return k;
                end if;
        end do:
end proc: # R. J. Mathar, Jul 08 2012

Crossrefs

Cf. A008908, A066906, A070165, A033491.

Sequence in context: A025549 A124013 A135584 * A340821 A091323 A174641

Adjacent sequences: A174535 A174536 A174537 * A174539 A174540 A174541

Keyword

nonn

Author

Michel Lagneau, Mar 21 2010

Extensions

Edited by R. J. Mathar, Jul 08 2012

Status

approved