A355601 a(1) = 47. For n > 1, a(n) = smallest prime q such that q^(a(n-1)-1) == 1 (mod a(n-1)^2).

47, 53, 521, 6037, 3347, 4931, 105667, 1131259, 4739509, 175166071, 3834885547

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 = 15 of A249162.

Cf. A355597, A355598, A355599, A355600, A355602.

Programs

Mathematica

nxt[a_]:=Module[{q=3},While[PowerMod[q,a-1,a^2]!=1,q=NextPrime[q]];q]; NestList[ nxt,47,10] (* The program will take a long time to run. *) (* Harvey P. Dale, Jan 31 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(47, 20) \\ Print initial 20 terms of sequence