A245671 3*x + 1 sequence starting at 1729.

1729, 5188, 2594, 1297, 3892, 1946, 973, 2920, 1460, 730, 365, 1096, 548, 274, 137, 412, 206, 103, 310, 155, 466, 233, 700, 350, 175, 526, 263, 790, 395, 1186, 593, 1780, 890, 445, 1336, 668, 334, 167, 502, 251, 754, 377, 1132, 566, 283, 850, 425, 1276, 638

Offset: 0

Author

Vincenzo Librandi, Jul 29 2014

Keywords

• nonn
• easy

Comments

1729 is known as the Hardy-Ramanujan number.

This sequence includes all those starting from the odd numbers: 5, 23, 35, 53, 61, 103, 137, 155, 167, 175, 233, 251, 263, 283, 319, 325, 365, 377, 395, 425, 433, 445, 479, 577, 593, 719, 911, 973, 1079, 1297, 1367, 1619.

Reaches a power of 2 at a(100) = 16. - Alonso del Arte, May 30 2015

Links

• Vincenzo Librandi, Table of n, a(n) for n = 0..200
• Index entries for sequences related to 3x+1 (or Collatz) problem

Crossrefs

Row 1729 of A347270.

Cf. A001235.

3*x+1 sequence starting at k: A008884 (k = 27), A008880 (k = 33), A008878 (k = 39), A008883 (k = 51), A008877 (k = 57), A008874 (k = 63), A008876 (k = 81), A008879 (k = 87), A008875 (k = 95), A008873 (k = 97), A008882 (k = 99), this sequence (k = 1729).

Programs

Magma

[n eq 1 select 1729 else IsOdd(Self(n-1)) select 3*Self(n-1)+1 else Self(n-1) div 2: n in [1..100]];

Mathematica

NestList[If[EvenQ[#], #/2, 3# + 1] &, 1729, 100]

Formula

a(0) = 1729, a(n) = 3*a(n-1) + 1 if a(n-1) is odd, a(n) = a(n-1)/2 otherwise. - Alois P. Heinz, Jul 29 2014