login
A275968
Smaller of two consecutive primes p and q such that c(p) = c(q), where c(n) = A008908(n) is the length of x, f(x), f(f(x)), ... , 1 in the Collatz conjecture.
1
173, 409, 419, 421, 439, 487, 521, 557, 571, 617, 761, 887, 919, 1009, 1039, 1117, 1153, 1171, 1217, 1327, 1373, 1549, 1559, 1571, 1657, 1693, 1709, 1721, 1733, 1783, 1831, 1861, 1901, 1993, 1997, 2053, 2089, 2339, 2393, 2521, 2539, 2647, 2657, 2677, 2693, 2777
OFFSET
1,1
COMMENTS
If x is even f(x) = x/2 else f(x) = 3x + 1.
LINKS
EXAMPLE
a(1) = p = 173; q = 179
c(p) = c(q) = 32
MATHEMATICA
t = Table[Length@ NestWhileList[If[EvenQ@ #, #/2, 3 # + 1] &, n, # != 1 &] - 1, {n, 10^4}]; Prime@ Flatten@ Position[#, k_ /; Length@ k == 1] &@ Map[Union@ Part[t, #] &, #] &@ Partition[#, 2, 1] &@ Prime@ Range@ 410 (* Michael De Vlieger, Sep 01 2016 *)
PROG
(PARI) A008908(n)=my(c=1); while(n>1, n=if(n%2, 3*n+1, n/2); c++); c
t=A008908(p=2); forprime(q=3, 1e4, tt=A008908(q); if(t==tt, print1(p", ")); p=q; t=tt) \\ Charles R Greathouse IV, Sep 01 2016
(Python)
import sympy
def lcs(n):
....a=1
....while n>1:
........if n%2==0:
............n=n//2
........else:
............n=(3*n)+1
........a=a+1
....return(a)
m=2
while m>0:
....n=sympy.nextprime(m)
....if lcs(m)==lcs(n):
........print(m, )
....m=n
# Abhiram R Devesh, Sep 02 2016
CROSSREFS
Cf. A006577 (Collatz trajectory lengths), A078417, A008908.
Sequence in context: A060332 A142022 A130338 * A142782 A142250 A059243
KEYWORD
nonn,easy
AUTHOR
Abhiram R Devesh, Aug 15 2016
STATUS
approved