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A087229
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Exponent of p=2 in 12n+4 = 3(4n+1)+1.
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3
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2, 4, 2, 3, 2, 6, 2, 3, 2, 4, 2, 3, 2, 5, 2, 3, 2, 4, 2, 3, 2, 8, 2, 3, 2, 4, 2, 3, 2, 5, 2, 3, 2, 4, 2, 3, 2, 6, 2, 3, 2, 4, 2, 3, 2, 5, 2, 3, 2, 4, 2, 3, 2, 7, 2, 3, 2, 4, 2, 3, 2, 5, 2, 3, 2, 4, 2, 3, 2, 6, 2, 3, 2, 4, 2, 3, 2, 5, 2, 3, 2, 4, 2, 3, 2, 10, 2, 3, 2, 4, 2, 3, 2, 5, 2, 3, 2, 4, 2, 3, 2, 6, 2, 3, 2, 4
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OFFSET
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0,1
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COMMENTS
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In the Collatz trajectory of m=4n+1, the first 3x+1 step is followed by a(n) consecutive divide-by-2 steps.
Large shifted overlaps with A085058.
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LINKS
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FORMULA
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EXAMPLE
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n=85: m = 4*n + 1 = 4*85 + 1 = 341, whose Collatz trajectory begins with 341 -> 1024 followed by a(85)=10 consecutive halving steps.
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MATHEMATICA
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Table[Part[Part[FactorInteger[12*w+4], 1], 2], {w, 0, 100}]
Table[IntegerExponent[12*n + 4, 2], {n, 0, 100}] (* Amiram Eldar, Feb 03 2022 *)
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PROG
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(Perl) # In 4*n+1 (n>0), find position of first bit that will repeat.
sub a {
my $nv= ((shift() << 2) | 1);
my $bp= 1;
while (($nv & 1) xor ($nv & 2)) {
$nv>>= 1;
$bp++;
}
return $bp;
}
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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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