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A270814
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a(1)=0; thereafter a(2k)=k+a(k), a(2k+1)=6k+4+a(6k+4).
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3
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0, 1, 46, 3, 31, 49, 281, 7, 330, 36, 248, 55, 106, 288, 679, 15, 197, 339, 500, 46, 127, 259, 610, 67, 633, 119, 101413, 302, 413, 694, 101073, 31, 808, 214, 505, 357, 498, 519, 2305, 66, 101290, 148, 1295, 281, 452, 633, 100932, 91, 757, 658, 1079, 145, 346, 101440, 102261, 330, 1596, 442, 2128
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OFFSET
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1,3
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COMMENTS
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In other words, a(n) = n/2 + a(n/2) if n even, a(n) = 3n+1+a(3n+1) if n odd.
This sequence was inspired by the Collatz problem (A006577).
The Collatz rule is as follows: If n is even, divide it by 2, otherwise multiply it by 3 and add 1 (A006370).
For example, starting with n = 3, one gets the sequence 3, 10, 5, 16, 8, 4, 2, 1. So a(3) = 10 + 5 + 16 + 8 + 4 + 2 + 1 = 46. (End) [Comment edited by N. J. A. Sloane, Apr 25 2016]
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LINKS
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MAPLE
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local a, traj ;
a := 0 ;
traj := n ;
while traj > 1 do
if type(traj, 'even') then
traj := traj/2 ;
else
traj := 3*traj+1 ;
end if;
a := a+traj ;
end do:
return a;
end proc:
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PROG
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(PARI) a(n) = my(ret=n-1); while((n>>=valuation(n, 2)) > 1, ret+=5*n+2; n=3*n+1); ret; \\ Kevin Ryde, Dec 10 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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