login
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.
2
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,...
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
KEYWORD
nonn
AUTHOR
Michel Lagneau, Mar 21 2010
EXTENSIONS
Edited by R. J. Mathar, Jul 08 2012
STATUS
approved