A355599 a(1) = 29. For n > 1, a(n) = smallest prime q such that q^(a(n-1)-1) == 1 (mod a(n-1)^2).

29, 41, 313, 1499, 941, 12011, 6287, 52301, 50077, 137743, 1274353, 46303409, 89018221, 687655393, 7462816891, 30345828679, 2526553938241, 48757253891971

Offset

1,1

Comments

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

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

Links

Table of n, a(n) for n=1..18.

Formula

a(n) = A355658(A000720(a(n-1))). - Max Alekseyev, Nov 07 2025

Prog

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

Crossrefs

Row n = 10 of A249162.

Cf. A355597, A355598, A355600, A355601, A355602.

Sequence in context: A238666 A106019 A181622 * A086149 A344515 A066502

Adjacent sequences: A355596 A355597 A355598 * A355600 A355601 A355602

Keyword

nonn,hard,more

Author

Felix Fröhlich, Jul 09 2022

Extensions

a(16)-a(18) from Max Alekseyev, Nov 07 2025

Status

approved