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A049194 Number of digits in n-th term of A001387. 3
1, 2, 3, 6, 8, 12, 18, 27, 39, 58, 85, 125, 183, 269, 394, 578, 847, 1242, 1820, 2668, 3910, 5731, 8399, 12310, 18041, 26441, 38751, 56793, 83234, 121986, 178779, 262014, 384000, 562780, 824794, 1208795, 1771575, 2596370, 3805165, 5576741 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

REFERENCES

Peter A. Hendriks, "A binary variant of Conway's audioactive sequence", lecture at 1192nd meeting of WWWW, Groningen, The Netherlands (Jul 15 1999).

LINKS

Table of n, a(n) for n=1..40.

T. Sillke, The binary form of Conway's sequence

FORMULA

a(n) = (8/9 + (1/18)*(748 - 36*sqrt(93))^(1/3) + (1/18)*(748 + 36*sqrt(93))^(1/3)) * (1/3 + (1/6)*(116 - 12*sqrt(93))^(1/3) + (1/6)*(116 + 12*sqrt(93))^(1/3))^n

The number of digits is equal to c*l^n rounded down to the nearest integer, where c and l are the real roots of 3x^3-8x^2+5x-1 and x^3-x^2-1 respectively, for all n except n=2 and n=3.

MATHEMATICA

CoefficientList[Series[(1+x+x^3-x^4-x^5)/(1-x-x^2+x^5), {x, 0, 50}], x] (* Peter J. C. Moses, Jun 21 2013 *)

PROG

(PARI) a(n) = if (n==3, 3, if (n==4, 6, floor((8/9 + (1/18)*(748 - 36*sqrt(93))^(1/3) + (1/18)*(748 + 36*sqrt(93))^(1/3)) * (1/3 + (1/6)*(116 - 12*sqrt(93))^(1/3) + (1/6)*(116 + 12*sqrt(93))^(1/3))^(n-1)))) \\ Michel Marcus, Mar 04 2013

CROSSREFS

Cf. A001387.

Sequence in context: A133582 A085642 A270738 * A058298 A299758 A303703

Adjacent sequences:  A049191 A049192 A049193 * A049195 A049196 A049197

KEYWORD

base,easy,nonn

AUTHOR

Olivier Gérard.

EXTENSIONS

More terms and formulas supplied by Gerton Lunter (gerton(AT)math.rug.nl)

STATUS

approved

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Last modified April 20 03:36 EDT 2019. Contains 322294 sequences. (Running on oeis4.)