A355600 a(1) = 37. For n > 1, a(n) = smallest prime q such that q^(a(n-1)-1) == 1 (mod a(n-1)^2).

37, 691, 19181, 5849, 18503, 37853, 478741, 18401827, 571007279, 5860639859

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 = 4.

Crossrefs

Row n = 12 of A249162.

Cf. A355597, A355598, A355599, A355601, A355602.

Programs

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(37, 20) \\ Print initial 20 terms of sequence