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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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified September 23 02:41 EDT 2021. Contains 347609 sequences. (Running on oeis4.)