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A000229 a(n) is the least number such that the n-th prime is the least quadratic nonresidue for a(n) (a(n) is always a prime).
(Formerly M2684 N1074)
3, 7, 23, 71, 311, 479, 1559, 5711, 10559, 18191, 31391, 422231, 701399, 366791, 3818929, 9257329, 22000801, 36415991, 48473881, 175244281, 120293879, 427733329, 131486759, 3389934071, 2929911599, 7979490791, 36504256799, 23616331489, 89206899239, 121560956039 (list; graph; refs; listen; history; text; internal format)



For n>1, a(n) = prime(k), where k is the smallest number such that A053760(k) = prime(n).

One could make a case for setting a(1)=2, but a(1)=3 seems more in keeping with the spirit of the sequence.


N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).


N. J. A. Sloane, Table of n, a(n) for n = 1..38 (from the web page of Tomás Oliveira e Silva)

H. J. Godwin, On the least quadratic non-residue, Proc. Camb. Phil. Soc., 61 (3) (1965), 671-672.

A. J. Hanson, G. Ortiz, A. Sabry and Y.-T. Tai, Discrete Quantum Theories, arXiv preprint arXiv:1305.3292, 2013

A. J. Hanson, G. Ortiz, A. Sabry, Y.-T. Tai, Discrete quantum theories, (a different version). (To appear in J. Phys. A: Math. Theor., 2014). http://www.cs.indiana.edu/~sabry/papers/saskatoon-talk.pdf

Tomás Oliveira e Silva, Least primitive root of prime numbers

Hans Salié, Uber die kleinste Primzahl, die eine gegebene Primzahl als kleinsten positiven quadratischen Nichtrest hat, Math. Nachr. 29 (1965) 113-114.


a(2)=7 because the second prime is 3 and 3 is the least quadratic nonresidue for 7, 14, 17, 31, 34, ... and 7 is the least of these.


Cf. A025021, A053760. For records see A133435.

Differs from A002223, A045535 at 12th term.

Sequence in context: A066768 A225914 A062241 * A133435 A079061 A228724

Adjacent sequences:  A000226 A000227 A000228 * A000230 A000231 A000232




N. J. A. Sloane


Definition corrected by Melvin J. Knight (MELVIN.KNIGHT(AT)ITT.COM), Dec 08 2006



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Last modified November 28 11:41 EST 2015. Contains 264557 sequences.