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A033493 Sum of numbers in trajectory of 3x+1 problem; first number n. 15
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; text; internal format)
OFFSET

1,2

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. - Alonso del Arte, Apr 10 2009

a(n) = sum (A070165(k): 1 <= k <= A006577(n)). - Reinhard Zumkeller, Oct 08 2011

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Collatz Problem

Wikipedia, Collatz conjecture

Index entries for sequences related to 3x+1 (or Collatz) problem

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. - Alonso del Arte, Apr 10 2009

MATHEMATICA

collatz[1] = 1; collatz[n_Integer?OddQ] := 3n + 1; collatz[n_Integer?EvenQ] := n/2; Table[-1 + Plus @@ FixedPointList[collatz, n], {n, 60}] (* Alonso del Arte, Apr 10 2009 *)

PROG

(Haskell)

a033493 = sum . a070165_row  -- Reinhard Zumkeller, Oct 08 2011

(Python)

def a(n):

....if n==1: return 1

....l=[n, ]

....while True:

........if n%2==0: n/=2

........else: n = 3*n + 1

........l+=[n, ]

........if n<2: break

....return sum(l)

print [a(n) for n in xrange(1, 101)] # Indranil Ghosh, Apr 14 2017

CROSSREFS

Apart from initial term, exactly the same as A049074. - Alonso del Arte, Apr 10 2009

Cf. A006370.

Sequence in context: A049524 A270748 A322363 * A094045 A033494 A079837

Adjacent sequences:  A033490 A033491 A033492 * A033494 A033495 A033496

KEYWORD

nonn

AUTHOR

Jeff Burch

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 del Arte, Apr 10 2009

STATUS

approved

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Last modified November 21 06:00 EST 2019. Contains 329350 sequences. (Running on oeis4.)