A174538 - OEIS

%I #10 Jul 09 2012 07:52:08

%S 3,3,3,60,246,560,560,560,4722,4722,6032,6666,13956,13956,13956,13956,

%T 13956,13956,13956,13956,13956,13956,13956,13956,81488,81488,81488,

%U 83840,89535,89535,89535,282880,282984,282984,282984,282984

%N 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.

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

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

%H Donovan Johnson, <a href="/A174538/b174538.txt">Table of n, a(n) for n = 1..619</a> (terms <= 10^10)

%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>

%e 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.

%p A174538 := proc(n)

%p         local k,allp;

%p         for k from 1 do

%p                 allp := true;

%p                 for i from 0 to n-1 do

%p                         if not isprime(A006577(k+i)) then

%p                                 allp := false;

%p                                 break;

%p                         end if;

%p                 end do:

%p                 if allp then

%p                         return k;

%p                 end if;

%p         end do:

%p end proc: # _R. J. Mathar_, Jul 08 2012

%Y Cf. A008908, A066906, A070165, A033491.

%K nonn

%O 1,1

%A _Michel Lagneau_, Mar 21 2010

%E Edited by _R. J. Mathar_, Jul 08 2012