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Search: id:A005574
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| A005574 |
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Numbers n such that n^2 + 1 is prime.
(Formerly M1010)
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+0
72
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| 1, 2, 4, 6, 10, 14, 16, 20, 24, 26, 36, 40, 54, 56, 66, 74, 84, 90, 94, 110, 116, 120, 124, 126, 130, 134, 146, 150, 156, 160, 170, 176, 180, 184, 204, 206, 210, 224, 230, 236, 240, 250, 256, 260, 264, 270, 280, 284, 300, 306, 314, 326, 340, 350
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Hardy and Littlewood conjectured that the asymptotic number of elements in this sequence not exceeding n is approximately c*sqrt(n)/ln(n) for some constant c. - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 06 2006
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REFERENCES
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R. K. Guy, "Unsolved Problems in Number Theory", 3rd edition, A2
G. H. Hardy and E. M. Wright, An Introduction to the Theory of Numbers, 5th ed., Oxford Univ. Press, 1979, th. 17.
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
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T. D. Noe, Table of n, a(n) for n=1..10000
F. Ellermann, Primes of the form (m^2)+1 up to 10^6
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Link to a section of The World of Mathematics.
Eric Weisstein's World of Mathematics, Near-Square Prime
Marek Wolf, Search for primes of the form m^2+1
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MATHEMATICA
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Select[Range[350], PrimeQ[ #^2 + 1] &] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 06 2006
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CROSSREFS
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a(n) = A090693(n)-1.
Cf. A002522, A001912, A002496, A062325, A090693.
Cf. A000068, A006314, A006313, A006315, A006316, A056994, A056995
Sequence in context: A104692 A066755 A089238 this_sequence A109807 A125964 A139544
Adjacent sequences: A005571 A005572 A005573 this_sequence A005575 A005576 A005577
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KEYWORD
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nonn,easy,nice
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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