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A076227
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Number of surviving Collatz residues mod 2^n.
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0
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1, 1, 1, 2, 3, 4, 8, 13, 19, 38, 64, 128, 226, 367, 734, 1295, 2114, 4228, 7495, 14990, 27328, 46611, 93222, 168807, 286581, 573162, 1037374, 1762293, 3524586, 6385637, 12771274, 23642078, 41347483, 82694966, 151917636, 263841377, 527682754, 967378591, 1934757182, 3611535862
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| Number of residue classes in which A074473(m) is not constant.
The ratio of numbers of inhomogenous r-classes versus uniform-classes enumerated here increases with n and tends to 0. For n large enough ratio < a(16)/65536=2114/65536 ~ 3.23 per cent.
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LINKS
| Tomás Oliveira e Silva, Computational verification of the 3x+1 conjecture
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EXAMPLE
| n=6: Modulo 64, eight residue classes were counted: r=7, 15, 27, 31, 39, 47, 59, 63. See A075476-A075483. For other 64-8=56 r-classes u(q)=A074473(64k+q) is constant: in 32 class u(q)=2, in 16 classes u(q)=4, in 4 classes u(q)=7 and in 4 cases u(q)=9. E.g. for r=11, 23, 43, 55 A047473(64k+r)=9 independently of k.
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PROG
| (C) /* call as follows: uint64_t s=survives(0, 1, 1, 0, bits); */
uint64_t survives(uint64_t r, uint64_t m, uint64_t lm, int p2, int fp2)
{
while(!(m&1) && (m>=lm)) {
if(r&1) { r+=(r+1)>>1; m+=m>>1; }
else { r>>=1; m>>=1; }
}
if(m<lm) { return 0; }
if(p2==fp2) { return 1; }
return survives(r, m<<1, lm<<1, p2+1, fp2)
+ survives(r+m, m<<1, lm<<1, p2+1, fp2);
}
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CROSSREFS
| Cf. A006370, A074473, A075476-A075483.
Sequence in context: A034776 A068791 A126042 * A186272 A092075 A091415
Adjacent sequences: A076224 A076225 A076226 * A076228 A076229 A076230
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KEYWORD
| more,nonn
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AUTHOR
| Labos E. (labos(AT)ana.sote.hu), Oct 01 2002
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EXTENSIONS
| New terms to n=39 and C program by Phil Carmody (pc+oeis(AT)asdf.org), Sep 08 2011
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