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A065840
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Numbers n such that the first n quaternary digits found in the base-10 expansion of Pi form a prime (when the decimal point is ignored).
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12
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1, 2, 3, 5, 10, 19, 72, 115, 220, 315, 375, 12408
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OFFSET
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1,2
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COMMENTS
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In other words, take the decimal expansion of Pi, drop any digits greater than 4, omit the decimal point and look for prefixes in the resulting string which form base-4 primes.
Numbers n such that A065838(n) is prime.
The next term in the sequence, if it exists, is greater than 10000. - Nathaniel Johnston, Nov 15 2010
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LINKS
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EXAMPLE
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E.g., the first a(5) or 10 quaternary digits of Pi are 31.12332323{4} and 3112332323{4} is the prime 880571{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 || p[[ # ]] == 2 || p[[ # ]] == 3 & ]]]; Do[ If[ PrimeQ[ FromDigits[ Take[p, n], 4]], Print[ n]], {n, 1, 4000} ]
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CROSSREFS
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KEYWORD
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nonn,base,hard
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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