A002199 -id:A002199

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Search: a002199 -id:a002199

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A071894

Largest positive primitive root (<p) of n-th prime p.

+10
10

1, 2, 3, 5, 8, 11, 14, 15, 21, 27, 24, 35, 35, 34, 45, 51, 56, 59, 63, 69, 68, 77, 80, 86, 92, 99, 101, 104, 103, 110, 118, 128, 134, 135, 147, 146, 152, 159, 165, 171, 176, 179, 189, 188, 195, 197, 207, 214, 224, 223, 230, 237, 234, 248, 254, 261, 267, 269, 272

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,2

REFERENCES

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards Applied Math. Series 55, 1964 (and various reprintings), p. 864.

R. Osborn, Tables of All Primitive Roots of Odd Primes Less Than 1000, Univ. Texas Press, 1961.

LINKS

T. D. Noe, Table of n, a(n) for n=1..10000

M. Abramowitz and I. A. Stegun, eds., Handbook of Mathematical Functions, National Bureau of Standards, Applied Math. Series 55, Tenth Printing, 1972 [alternative scanned copy].

FORMULA

a(n) = prime(n) - A002199(n) - T. D. Noe, Oct 24 2005

MATHEMATICA

f[n_] := Block[{k = Prime[n] - 1, p = Prime[n], t = Table[i, {i, 1, Prime[n] - 1}]}, While[ Union[ PowerMod[ k, t, p]] != t, k-- ]; k]; Table[ f[n], {n, 1, 60}]

PROG

(PARI) a(n) = my(p=prime(n)); forstep(q=p-1, 1, -1, if(znorder(Mod(q, p))==eulerphi(p), return(q))); \\ Michel Marcus, Sep 28 2023

CROSSREFS

A diagonal of triangle in A060749.

Cf. A000040, A001918 (least positive primitive root), A002199.

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane, Jun 11, 2002

EXTENSIONS

More terms from Robert G. Wilson v, Jun 11 2002

STATUS

approved

A033947

Smallest primitive root (in absolute value) of n-th prime.

+10
0

1, -1, 2, -2, 2, 2, 3, 2, -2, 2, 3, 2, 6, 3, -2, 2, 2, 2, 2, -2, 5, -2, 2, 3, 5, 2, -2, 2, 6, 3, 3, 2, 3, 2, 2, -5, 5, 2, -2, 2, 2, 2, -2, 5, 2, -2, 2, 3, 2, 6, 3, -2, 7, -3, 3, -2, 2, -2, 5, 3, 3, 2, 5, -2, 10, 2, 3, 10, 2, 2, 3, -2, -2, 2, 2, -2, 2, 5, 3, 21, 2, 2, -5, 5, -5, 2, 3, 13, 2, -2

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

LINKS

Table of n, a(n) for n=1..90.

CROSSREFS

Cf. A001918, A002199, A000040.

KEYWORD

sign

AUTHOR

Calculated by Jud McCranie

STATUS

approved

A246603

-a(n) is the greatest negative primitive root that all of the first n primes share.

+10
0

1, 1, 7, 37, 37, 37, 37, 1423, 10987, 13297, 219277, 219277, 669463, 2215987, 7841563, 33376753, 54444163, 112545673, 267625087, 1676296087, 2772262903, 2782012963, 4341199657, 34694683237, 39965586763, 232265913427, 1879768081657, 1879768081657

(list; graph; refs; listen; history; text; internal format)

OFFSET

1,3

REFERENCES

Don Reble, Posting to Sequence Fans Mailing List, Sep 07 2014

LINKS

Table of n, a(n) for n=1..28.

CROSSREFS

Cf. A002199, A128895.

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Sep 09 2014

STATUS

approved

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