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Search: id:A045707
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| A045707 |
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Primes with first digit 1. |
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+0
2
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| 11, 13, 17, 19, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 179, 181, 191, 193, 197, 199, 1009, 1013, 1019, 1021, 1031, 1033, 1039, 1049, 1051, 1061, 1063, 1069, 1087, 1091, 1093, 1097, 1103, 1109, 1117, 1123, 1129, 1151
(list; graph; listen)
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OFFSET
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0,1
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REFERENCES
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Cohen, Daniel I. A. and Katz, Talbot M., Prime numbers and the first digit phenomenon. J. Number Theory 18 (1984), 261-268.
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FORMULA
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Comment from Gary McGuire, Dec 22 2004: Cohen and Katz show that the set of primes with first digit 1 has no natural density, but has supernatural/Dirichlet density log_{10} (2) ~= 0.3, the primes with first digit 2 have (supernatural) density log_{10} (3/2) ~=0.176, .... and the primes with first digit 9 have density log_{10} (10/9) ~= 0.046. This would seem to explain the first digit phenomenon. Note that sum_{k=1}^9 log_{10} (k+1)/k = 1.
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MATHEMATICA
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Select[ Table[ Prime[ n ], {n, 1, 500} ], First[ IntegerDigits[ # ] ]==1& ]
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CROSSREFS
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Cf. A000040, A045708, A045709, etc.
Sequence in context: A132244 A087201 A068492 this_sequence A032591 A088265 A090149
Adjacent sequences: A045704 A045705 A045706 this_sequence A045708 A045709 A045710
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KEYWORD
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nonn,base
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AUTHOR
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Felice Russo (felice.russo(AT)katamail.com)
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EXTENSIONS
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More terms from Erich Friedman (erich.friedman(AT)stetson.edu).
Cohen-Katz reference from Victor Miller, Dec 21, 2004.
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