A355598 a(1) = 3. For n > 1, a(n) = smallest prime q such that q^(a(n-1)-1) == 1 (mod a(n-1)^2).

3, 17, 131, 659, 503, 9833, 49603, 327317, 13900147, 144229223, 5872276013

Offset: 1

Author

Felix Fröhlich, Jul 09 2022

Keywords

• nonn
• hard
• more

Comments

Is this overall an increasing sequence or does it enter a cycle?

The sequence decreases for the first time at n = 5.

Crossrefs

Row n = 2 of A249162.

Cf. A355597, A355599, A355600, A355601, A355602.

Programs

Mathematica

sp[n_]:=Module[{p=2},While[PowerMod[p,n-1,n^2]!=1,p=NextPrime[p]];p]; NestList[sp,3,8] (* Harvey P. Dale, Jul 23 2023 *)

PARI

seq(start, terms) = my(x=start, i=1); print1(start, ", "); while(1, forprime(q=1, , if(Mod(q, x^2)^(x-1)==1, print1(q, ", "); x=q; i++; if(i >= terms, break({2}), break))))
seq(3, 20) \\ Print initial 20 terms of sequence