A181921 The smallest positive integer that produces exactly n primes in a Collatz trajectory.

2, 5, 3, 15, 11, 7, 19, 43, 67, 89, 39, 127, 123, 223, 111, 351, 175, 155, 103, 63, 107, 71, 47, 31, 27, 97, 193, 171, 231, 487, 1087, 763, 2223, 2143, 1263, 1071, 4011, 6919, 8127, 13183, 6591, 6943, 6171, 10971, 46443, 48927, 35295, 17647, 70589, 47059

Offset

1,1

Links

Reinhard Zumkeller and Jud McCranie, Table of n, a(n) for n = 1..92 (first 75 numbers from Reinhard Zumkeller)

Eric Weisstein's World of Mathematics, Collatz Problem

Wikipedia, Collatz conjecture

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

Example

a(6) = 7 because the Collatz trajectory of 7 is {7, 22, 11, 34, 17, 52, 26, 13, 40, 20, 10, 5, 16, 8, 4, 2, 1}, containing 6 primes {7, 11, 17, 13, 5, 2}, and 7 is the smallest positive integer for which exactly 6 primes occur via this trajectory.

Mathematica

Collatz[n_] := NestWhileList[If[EvenQ[#], #/2, 3 # + 1] &, n, # > 1 &]; nn = 50; t = Table[0, {nn}]; t[[1]] = 2; todo = nn - 1; n = 3; While[todo > 0, ps = Length[Select[Collatz[n], PrimeQ]]; If[ps <= nn && t[[ps]] == 0, t[[ps]] = n; todo--]; n = n + 2]; t (* T. D. Noe, Apr 02 2012 *)
With[{lst=Table[Count[NestWhileList[If[EvenQ[#], #/2, 3#+1]&, n, #>1&], _?PrimeQ], {n, 71000}]}, Table[Position[lst, k, 1, 1], {k, 50}]//Flatten] (* Harvey P. Dale, Sep 08 2018 *)

Prog

(PARI) np(n)=my(t=1); while(n>2, t+=isprime(n); if(n%2, n+=n>>1+1, n>>=1)); t
v=vector(40); n=1; while(1, t=np(n++); if(t<=#v&&v[t]==0, v[t]=n; if(vecmin(v), return(v)))) \\ Charles R Greathouse IV, Apr 01 2012
(Haskell)
import Data.List (elemIndex)
import Data.Maybe (fromJust)
a181921 = (+ 1) . fromJust . (`elemIndex` a078350_list)
-- Reinhard Zumkeller, Apr 03 2012

Crossrefs

Cf. A055509, A078350.

Sequence in context: A245612 A243066 A368316 * A282575 A002565 A063703

Adjacent sequences: A181918 A181919 A181920 * A181922 A181923 A181924

Keyword

nonn

Author

G. L. Honaker, Jr., Apr 01 2012

Extensions

a(13)-a(50) from Charles R Greathouse IV, Apr 01 2012

Status

approved