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

Author

Michel Lagneau, Mar 21 2010

Keywords

• nonn

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,...

Examples

			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.
		

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

Crossrefs

Cf. A008908, A066906, A070165, A033491.

Programs

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

Extensions

Edited by R. J. Mathar, Jul 08 2012