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Search: id:A065832
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| A065832 |
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Numbers n such that the first n binary digits found in the base-10 expansion of pi form a prime (when the decimal point is ignored). |
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+0
2
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| 2, 4, 10, 24, 29, 34, 43, 62, 76, 351, 778, 2736, 4992, 7517
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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In other words, take the decimal expansion of pi, drop any digits greater than 1, omit the decimal point and look for prefixes in the resulting string which form base-2 primes.
Numbers n such that A065830(n) is prime.
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EXAMPLE
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E.g. the first a(3) or 10 binary digits of pi are 1101110001{2} which is prime 881{10}.
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MATHEMATICA
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p = First[ RealDigits[ Pi, 10, 10^5]]; p = p[[ Select[ Range[10^5], p[[ # ]] == 0 || p[[ # ]] == 1 & ]]]; Do[ If[ PrimeQ[ FromDigits[ Take[p, n], 2]], Print[n]], {n, 1, Length[p] } ]
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CROSSREFS
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Cf. A065828 up to A065840, A000796, A011545, A011546, A055143, A005042, A060421, A039954, A048796.
Sequence in context: A130967 A148087 A156806 this_sequence A072753 A009884 A032023
Adjacent sequences: A065829 A065830 A065831 this_sequence A065833 A065834 A065835
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KEYWORD
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nonn,base,hard
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AUTHOR
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Patrick De Geest (pdg(AT)worldofnumbers.com), Nov 24 2001.
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Nov 30 2001
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