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A005574
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Numbers n such that n^2 + 1 is prime.
(Formerly M1010)
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82
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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, 384, 386, 396
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| Hardy and Littlewood conjectured that the asymptotic number of elements in this sequence not exceeding n is approximately c*sqrt(n)/log(n) for some constant c. - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 06 2006
Also, non-negative integers such that a(n)+i is a Gaussian prime. [Maciej Ireneusz Wilczynski, May 30 2011]
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REFERENCES
| J.-M. De Koninck, Ces nombres qui nous fascinent, Entry 166, p. 53, Ellipses, Paris 2008. - from Michel Lagneau (mn.lagneau2(AT)orange.fr), Feb 02 2010
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
| 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, Landaus Problems
Eric Weisstein's World of Mathematics, Power
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
| Select[Range[350], PrimeQ[ #^2 + 1] &] - Stefan Steinerberger (stefan.steinerberger(AT)gmail.com), Apr 06 2006
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PROG
| (PARI) isA005574(n) = isprime(n^2+1) [From Michael B. Porter (michael_b_porter(AT)yahoo.com), Mar 20 2010]
(MAGMA) [n: n in [0..1000] | IsPrime(n^2+1)] [From V. Librandi, Nov 18 2010]
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CROSSREFS
| a(n) = A090693(n)-1.
Cf. A002522, A001912, A002496, A062325, A090693, A000068, A006314, A006313, A006315, A006316, A056994, A056995
Sequence in context: A104692 A066755 A089238 * A109807 A191113 A125964
Adjacent sequences: A005571 A005572 A005573 * A005575 A005576 A005577
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KEYWORD
| nonn,easy,nice
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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