A007349 -id:A007349 - cp's OEIS frontend

A218766 Composite numbers with both 10 and -10 as primitive root.

289, 841, 3721, 4913, 9409, 11881, 12769, 22201, 24389, 32761, 37249, 52441, 54289, 66049, 72361, 83521, 97969, 113569, 151321, 187489, 212521, 226981, 259081, 292681, 332929, 351649, 491401, 502681, 674041, 707281, 734449, 877969, 885481, 908209, 912673

Offset: 1

Arkadiusz Wesolowski, Nov 05 2012

nonn

The powers of primes from A007349.

Intersection of A002808, A167797 and A167806.

			12769 = 113^2 belongs to this sequence because 113 is in A007349.

Arkadiusz Wesolowski, Table of n, a(n) for n = 1..10000
Eric Weisstein's World of Mathematics, Primitive Root

Cf. A007349.

lst = {}; r = 912673; Do[If[PrimeQ[i] && MultiplicativeOrder[10, i] == MultiplicativeOrder[-10, i] == i - 1, n = 2; While[(p = i^n) <= r, AppendTo[lst, p]; n++]], {i, Floor@Sqrt[r]}]; Sort[lst]

A381590 Primes with primitive root -100.

Original entry on oeis.org

3, 7, 19, 23, 31, 43, 47, 59, 67, 71, 83, 107, 131, 151, 163, 167, 179, 191, 199, 223, 227, 263, 283, 307, 311, 347, 359, 367, 379, 383, 419, 431, 439, 443, 467, 479, 487, 491, 499, 503, 523, 563, 571, 587, 599, 619, 631, 647, 659, 683, 719, 727, 743, 787, 811

Offset: 1

Davide Rotondo, Feb 28 2025

Union of long period primes (A006883) of the form 4k-1 and half period primes (A097443) of the form 4k-1.

Complement of A007349 in the union of A007348 and A001913. - Davide Rotondo, May 23 2025

Cf. A006883, A097443, A007349, A007348, A001913.

Select[Prime[Range[150]], MultiplicativeOrder[-100, #] == # - 1 &]  (* Amiram Eldar, Mar 02 2025 *)

is(n)=gcd(n,10)==1 && znorder(Mod(-100, n))==n-1 \\ Charles R Greathouse IV, Mar 01 2025

list(lim)=my(v=List([3])); forprime(p=7,lim, if(znorder(Mod(-100, p))==p-1, listput(v,p))); Vec(v) \\ Charles R Greathouse IV, Mar 01 2025

cp's OEIS Frontend

A218766 Composite numbers with both 10 and -10 as primitive root.

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