Density bounds for the problem. I. Treesearch method
Authors:
David Applegate and Jeffrey C. Lagarias
Journal:
Math. Comp. 64 (1995), 411426
MSC:
Primary 11B83; Secondary 11Y99
MathSciNet review:
1270612
Fulltext PDF Free Access
Abstract 
References 
Similar Articles 
Additional Information
Abstract: The function takes the values if x is odd and if x is even. Let a be any integer with . If counts the number of n with , then for all sufficiently large k, . If counts the number of n with which eventually reach a under iteration by T, then for sufficiently large x, . The proofs are computerintensive.
 [1]
David
Applegate and Jeffrey
C. Lagarias, Density bounds for the 3𝑥+1
problem. II. Krasikov inequalities, Math.
Comp. 64 (1995), no. 209, 427–438. MR 1270613
(95c:11025), http://dx.doi.org/10.1090/S00255718199512706132
 [2]
, On the distribution of trees, Experimental Math. (to appear).
 [3]
R.
E. Crandall, On the “3𝑥+1”
problem, Math. Comp. 32
(1978), no. 144, 1281–1292.
MR
0480321 (58 #494), http://dx.doi.org/10.1090/S00255718197804803213
 [4]
Ivan
Korec, A density estimate for the 3𝑥+1 problem, Math.
Slovaca 44 (1994), no. 1, 85–89. MR 1290275
(95h:11022)
 [5]
I.
Krasikov, How many numbers satisfy the 3𝑋+1
conjecture?, Internat. J. Math. Math. Sci. 12 (1989),
no. 4, 791–796. MR 1024983
(90k:11013), http://dx.doi.org/10.1155/S0161171289000979
 [6]
Jeffrey
C. Lagarias, The 3𝑥+1 problem and its generalizations,
Amer. Math. Monthly 92 (1985), no. 1, 3–23. MR 777565
(86i:11043), http://dx.doi.org/10.2307/2322189
 [7]
J.
C. Lagarias and A.
Weiss, The 3𝑥+1 problem: two stochastic models, Ann.
Appl. Probab. 2 (1992), no. 1, 229–261. MR 1143401
(92k:60159)
 [8]
Gary
T. Leavens and Mike
Vermeulen, 3𝑥+1 search programs, Comput. Math. Appl.
24 (1992), no. 11, 79–99. MR 1186722
(93k:68047), http://dx.doi.org/10.1016/08981221(92)90034F
 [9]
J.
W. Sander, On the (3𝑁+1)conjecture, Acta Arith.
55 (1990), no. 3, 241–248. MR 1067972
(91m:11052)
 [10]
Günther
Wirsching, An improved estimate concerning 3𝑛+1 predecessor
sets, Acta Arith. 63 (1993), no. 3,
205–210. MR 1218235
(94e:11018)
 [1]
 D. Applegate and J. C. Lagarias, Density bounds for the problem. II, Krasikov inequalities, Math. Comp. 64 (1995), 427438. MR 1270613 (95c:11025)
 [2]
 , On the distribution of trees, Experimental Math. (to appear).
 [3]
 R. E. Crandall, On the problem, Math. Comp. 32 (1978), 12811292. MR 0480321 (58:494)
 [4]
 I. Korec, A density estimate for the problem, Math. Slovaca 44 (1994), 8589. MR 1290275 (95h:11022)
 [5]
 I. Krasikov, How many numbers satisfy the conjecture?, Internat. J. Math. Math. Sci. 12 (1989), 791796. MR 1024983 (90k:11013)
 [6]
 J. C. Lagarias, The problem and its generalizations, Amer. Math. Monthly 92 (1985), 321. MR 777565 (86i:11043)
 [7]
 J. C. Lagarias and A. Weiss, The problem: Two stochastic models, Ann. Appl. Probab. 2 (1992), 229261. MR 1143401 (92k:60159)
 [8]
 G. T. Leavens and M. Vermeulen, search programs, Comput. Math. Appl. 24 (1992), no. 11, 7999. MR 1186722 (93k:68047)
 [9]
 J. W. Sander, On the conjecture, Acta Arith. 55 (1990), 241248. MR 1067972 (91m:11052)
 [10]
 G. Wirsching, An improved estimate concerning predecessor sets, Acta Arith. 63 (1993), 205210. MR 1218235 (94e:11018)
Similar Articles
Retrieve articles in Mathematics of Computation
with MSC:
11B83,
11Y99
Retrieve articles in all journals
with MSC:
11B83,
11Y99
Additional Information
DOI:
http://dx.doi.org/10.1090/S00255718199512706120
PII:
S 00255718(1995)12706120
Article copyright:
© Copyright 1995
American Mathematical Society
