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Search: id:A119377
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| A119377 |
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Numbers k such that the next k binary digits of Pi are odd primes with no leading zeros. |
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1
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| 2787, 6, 7, 23, 2, 3, 3, 8, 2, 2, 2, 5, 8, 2, 18, 9, 10, 413, 8, 3, 2, 4019, 14, 4, 2, 2, 11, 21, 4, 2, 3, 6, 2, 11, 3, 5, 19, 2, 6, 2, 4, 32, 2, 56, 31, 6, 7, 7, 2, 32, 20, 9, 10, 900, 2, 2, 2, 97, 5, 2, 8, 64, 3, 13, 3, 2, 6, 7, 15, 3, 2666, 7, 8, 3, 14, 3, 2, 2, 6, 5, 92, 17, 31, 4, 241, 78, 3
(list; graph; listen)
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OFFSET
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1,1
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COMMENT
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Partition the string of binary digits of Pi in such a way that each partition begins and ends with 1 (thus no leading or trailing zeros) and each such partition is prime.
Pi_2 = 1100100100001111110110101010001000100001011010001100001000..._2 (A004601).
If 2 is allowed as a member, then the sequence begins: 2787,2,5,6,2,2,2,39,5,8,2,18,9,10,2,153,2,6,2,18,7,7,12,2,2,2,2,....
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EXAMPLE
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a(1) represents the binary number 1100100100...(2767 terms)...0100000011 which equals the decimal number 7339860347...(819 terms)...8308318467 which is a prime.
a(2) represents the binary number 101001 which equals the decimal number 41, a prime.
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MATHEMATICA
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ps = First@ RealDigits[Pi, 2, 12010]; lst = {}; Do[k = 1; While[fd = FromDigits[ Take[ps, k], 2]; EvenQ@fd || ps[[k + 1]] == 0 || !PrimeQ@fd, k++ ]; AppendTo[lst, k]; ps = Drop[ps, k], {n, 87}]; lst
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CROSSREFS
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Cf. A004601, A068425, A117721, A065987, A119017.
Sequence in context: A046380 A154081 A099691 this_sequence A014895 A106300 A115471
Adjacent sequences: A119374 A119375 A119376 this_sequence A119378 A119379 A119380
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KEYWORD
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base,nonn
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AUTHOR
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Robert G. Wilson v (rgwv(AT)rgwv.com), Jul 24 2006
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