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.

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

Author

Abhiram R Devesh, Aug 15 2016

Keywords

• nonn
• easy

Comments

If x is even f(x) = x/2 else f(x) = 3x + 1.

Examples

			a(1) = p = 173; q = 179
c(p) = c(q) = 32
		

Links

• Abhiram R Devesh, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A006577 (Collatz trajectory lengths), A078417, A008908.

Programs

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 *)

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