A107439 a(1)=2, a(n) is the smallest prime > a(n-1) such that a(n) is a primitive root mod a(n-1) and vice versa.

2, 3, 5, 7, 17, 23, 89, 113, 137, 149, 163, 181, 191, 233, 257, 263, 277, 283, 397, 419, 421, 443, 449, 461, 463, 509, 557, 569, 593, 599, 613, 619, 701, 719, 821, 823, 829, 857, 863, 877, 919, 1097, 1103, 1117, 1171, 1181, 1193, 1213, 1237, 1259, 1361, 1367

Offset

1,1

Comments

if a(n) is 3 mod 4, then by quadratic reciprocity, if q is 3 mod 4, then either q is a square mod a(n) or vice versa, so a(n+1) must be 1 mod 4.

Links

Iain Fox, Table of n, a(n) for n = 1..10000

Example

a(5)=17 because 7 is a primitive root mod 17 and 17 (=3 mod 7) is a primitive root mod 7. Also a(5) is not 11 since 11 has order 3 mod 7, a(5) is not 13 since 13 has order 2 mod 7.

Prog

(PARI) first(n) = { my(res=vector(n)); res[1]=2; for(x=2, n, forprime(p=res[x-1]+1, , if(znorder(Mod(p, res[x-1]))==(res[x-1]-1) && znorder(Mod(res[x-1], p))==(p-1), res[x]=p; break()))); res; } \\ Iain Fox, Nov 29 2017

Crossrefs

Sequence in context: A164042 A248344 A060212 * A262836 A356475 A178382

Adjacent sequences: A107436 A107437 A107438 * A107440 A107441 A107442

Keyword

nonn

Author

John L. Drost, May 26 2005

Status

approved