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A076536 Image of n at the third step in the 3x+1 Problem: syr(3,n). 4
1, 2, 16, 4, 4, 5, 34, 1, 7, 8, 52, 10, 10, 11, 70, 2, 13, 14, 88, 16, 16, 17, 106, 3, 19, 20, 124, 22, 22, 23, 142, 4, 25, 26, 160, 28, 28, 29, 178, 5, 31, 32, 196, 34, 34, 35, 214, 6, 37, 38, 232, 40, 40, 41, 250, 7, 43, 44, 268, 46, 46, 47, 286, 8, 49, 50, 304, 52, 52, 53 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Also known as the Collatz Problem, Sysacuse Algorithm or Hailstone Problem. Let syr(m,n) be the image of n at the m-th step. for m=3,k>=0 we get: syr(3,8k)=k, syr(3,8k+1)=6k+1, syr(3,8k+2)=6k+2, syr(3,8k+3)=36k+16, syr(3,8k+4)=6k+4, syr(3,8k+5)=6k+4, syr(3,8k+6)=6k+5, syr(3,8k+7)=36k+34

REFERENCES

David Wells, Penguin Dictionary of Curious and Interesting Numbers.

LINKS

G. C. Greubel, Table of n, a(n) for n = 1..10000

Eric Weisstein's World of Mathematics, Collatz Problem

FORMULA

G.f.: x*(1 +2*x +16*x^2 +4*x^3 +4*x^4 +5*x^5 +34*x^6 +x^7 +5*x^8 +4*x^9 +20*x^10 +2*x^11 +2*x^12 +x^13 +2*x^14)/(1-x^8)^2.

EXAMPLE

1->4->2->1; 2->1->4->2; 3->10->5->16; ...

MATHEMATICA

Rest[CoefficientList[Series[(x +2x^2 +16x^3 +4x^4 +4x^5 +5x^6 +34x^7 + x^8 +5x^9 +4x^10 +20x^11 +2x^12 +2x^13 +x^14 +2x^15)/(1-x^8)^2, {x, 0, 80}], x]] (* G. C. Greubel, Oct 16 2018 *)

PROG

(PARI) x='x+O('x^80); Vec(x*(1 +2*x +16*x^2 +4*x^3 +4*x^4 +5*x^5 +34*x^6 +x^7 +5*x^8 +4*x^9 +20*x^10 +2*x^11 +2*x^12 +x^13 +2*x^14)/(1-x^8)^2) \\ G. C. Greubel, Oct 16 2018

(MAGMA) m:=80; R<x>:=PowerSeriesRing(Integers(), m); Coefficients(R!(x*(1 +2*x +16*x^2 +4*x^3 +4*x^4 +5*x^5 +34*x^6 +x^7 +5*x^8 +4*x^9 +20*x^10 +2*x^11 +2*x^12 +x^13 +2*x^14)/(1-x^8)^2)); // G. C. Greubel, Oct 16 2018

CROSSREFS

Cf. A006370 (n at step 1), A075884 (n at step 2).

Sequence in context: A095860 A070654 A036164 * A110009 A232503 A025586

Adjacent sequences:  A076533 A076534 A076535 * A076537 A076538 A076539

KEYWORD

easy,nonn

AUTHOR

Bruce Corrigan (scentman(AT)myfamily.com), Oct 18 2002

STATUS

approved

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Last modified August 10 04:38 EDT 2020. Contains 336368 sequences. (Running on oeis4.)