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%I #36 Sep 08 2022 08:46:09
%S 1729,5188,2594,1297,3892,1946,973,2920,1460,730,365,1096,548,274,137,
%T 412,206,103,310,155,466,233,700,350,175,526,263,790,395,1186,593,
%U 1780,890,445,1336,668,334,167,502,251,754,377,1132,566,283,850,425,1276,638
%N 3*x + 1 sequence starting at 1729.
%C 1729 is known as the Hardy-Ramanujan number.
%C 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.
%C Reaches a power of 2 at a(100) = 16. - _Alonso del Arte_, May 30 2015
%H Vincenzo Librandi, <a href="/A245671/b245671.txt">Table of n, a(n) for n = 0..200</a>
%H <a href="/index/3#3x1">Index entries for sequences related to 3x+1 (or Collatz) problem</a>
%F 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
%t NestList[If[EvenQ[#], #/2, 3# + 1] &, 1729, 100]
%o (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]];
%Y Row 1729 of A347270.
%Y Cf. A001235.
%Y 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).
%K nonn,easy
%O 0,1
%A _Vincenzo Librandi_, Jul 29 2014
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