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

1,1

Comments

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

Links

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

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

Adjacent sequences: A275965 A275966 A275967 * A275969 A275970 A275971

Keyword

nonn,easy

Author

Abhiram R Devesh, Aug 15 2016

Status

approved