primes in pi: 1, 2, 6, 38, 16208, 47577, 78073, ...
N. J. A. Sloane
njas at research.att.com
Sun Jul 23 13:40:36 CEST 2006
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Richard Guy said:
> It would be more natural (??) to do this in base 2.
>
> So here are two new(?) sequences for people to
> check and extend:
>
> The first
> 2, 8, 14, 18, ...
>
> digits in the binary representation of pi form the
> primes
> 3, 401, 25667, 410687, ...
>
> in decimal notation.
Me:
The binary expansion of Pi is A004601:
1,1,0,0,1,0,0,1,0,0,0,0,1,1,1,1,1,1,0,1,1,0,1,0,1,0,1,0,...
Converting first n bits to an integer gives A068425:
1,3,6,12,25,50,100,201,402,804,1608,3216,...
The primes here are A117721:
3,6588397,1686629713,26986075409,16703571626015105435307505830654230989, ...
and they occur for these values of n (A065987):
2,23,31,35,124,323,2787,5717,6506 (and that's all I have)
The latter sequence was computed by Bob Wilson.
Eric, can you extend it?
Richard, I seem to disagree with your results, but perhaps
I misunderstood your message?
Neil
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