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A181921 The smallest positive integer that produces exactly n primes in a Collatz trajectory. 3
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 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

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

Wikipedia, Collatz conjecture

Eric Weisstein's World of Mathematics, Collatz Problem

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 *)

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: A243506 A245612 A243066 * A002565 A063703 A109619

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

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Last modified November 22 20:02 EST 2014. Contains 249827 sequences.