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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified August 3 19:17 EDT 2021. Contains 346441 sequences. (Running on oeis4.)