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A065832
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Numbers k such that the first k binary digits found in the base-10 expansion of Pi form a prime (when the decimal point is ignored).
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2
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2, 4, 10, 24, 29, 34, 43, 62, 76, 351, 778, 2736, 4992, 7517, 22044, 40390
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OFFSET
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1,1
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COMMENTS
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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 k such that A065830(k) is prime.
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LINKS
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EXAMPLE
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The first a(3)=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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KEYWORD
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nonn,base,hard,more
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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