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A033493
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Sum of numbers in trajectory of 3x+1 problem; first number n.
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2
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1, 3, 49, 7, 36, 55, 288, 15, 339, 46, 259, 67, 119, 302, 694, 31, 214, 357, 519, 66, 148, 281, 633, 91, 658, 145, 101440, 330, 442, 724, 101104, 63, 841, 248, 540, 393, 535, 557, 2344, 106, 101331, 190, 1338, 325, 497, 679, 100979, 139, 806, 708, 1130, 197
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Given a power of two, the value in this sequence is the next higher Mersenne number, or a(2^m) = 2^(m + 1) - 1. [From Alonso Delarte (alonso.delarte(AT)gmail.com), Apr 10 2009]
a(n) = sum (A070165(k): 1 <= k <= A006577(n)). [Reinhard Zumkeller, Oct 08 2011]
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LINKS
| Reinhard Zumkeller, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, CollatzProblem
Wikipedia, Collatz conjecture
Index entries for sequences related to 3x+1 (or Collatz) problem
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EXAMPLE
| a(5) = 36 because the Ulam's conjecture trajectory sequence starting on 5 runs 5, 16, 8, 4, 2, 1 and therefore 5 + 16 + 8 + 4 + 2 + 1 = 36. [From Alonso Delarte (alonso.delarte(AT)gmail.com), Apr 10 2009]
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MATHEMATICA
| f[1] = 1; f[n_Integer?OddQ] := 3n + 1; f[n_Integer?EvenQ] := n/2; Table[ -1 + Plus @@ FixedPointList[f, n], {n, 60}] [From Alonso Delarte (alonso.delarte(AT)gmail.com), Apr 10 2009]
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PROG
| (Haskell)
a033493 = sum . a070165_row -- Reinhard Zumkeller, Oct 08 2011
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CROSSREFS
| Apart from initial term, exactly the same as A049074. [From Alonso Delarte (alonso.delarte(AT)gmail.com), Apr 10 2009]
Cf. A006370.
Sequence in context: A201698 A003029 A049524 * A094045 A033494 A079837
Adjacent sequences: A033490 A033491 A033492 * A033494 A033495 A033496
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KEYWORD
| nonn
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AUTHOR
| Jeff Burch (gburch(AT)erols.com)
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EXTENSIONS
| Corrected a(16) to 31 to match other powers of 2; removed duplicate value of a(48) = 139 because a(49) = 806 and not 139. Alonso Delarte (alonso.delarte(AT)gmail.com), Apr 10 2009
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