|
| |
|
|
A000229
|
|
a(n) is the least number such that the n-th prime is the least quadratic nonresidue (not necessarily coprime) modulo a(n).
(Formerly M2684 N1074)
|
|
8
|
|
|
|
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)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
Note that a(n) is always a prime.
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.
|
|
|
REFERENCES
|
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).
|
|
|
LINKS
|
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 [quant-ph], 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).
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.
|
|
|
EXAMPLE
|
a(2) = 7 because the second prime is 3 and 3 is the least quadratic nonresidue modulo 7, 14, 17, 31, 34, ... and 7 is the least of these.
|
|
|
MATHEMATICA
|
leastNonRes[p_] := For[q = 2, True, q = NextPrime[q], If[JacobiSymbol[q, p] != 1, Return[q]]]; a[1] = 3; a[n_] := For[pn = Prime[n]; k = 1, True, k++, an = Prime[k]; If[pn == leastNonRes[an], Print[n, " ", an]; Return[an]]]; Array[a, 20] (* Jean-François Alcover, Nov 28 2015 *)
|
|
|
CROSSREFS
|
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
|
|
|
KEYWORD
|
nonn,nice
|
|
|
AUTHOR
|
N. J. A. Sloane
|
|
|
EXTENSIONS
|
Definition corrected by Melvin J. Knight (MELVIN.KNIGHT(AT)ITT.COM), Dec 08 2006
|
|
|
STATUS
|
approved
|
| |
|
|
