A354426 Primes p such that q divides p^2 + p + 1, r divides q^2 + q + 1 and p divides r + 1 for some primes q and r.

2, 7, 79, 5569, 9829

Offset

1,1

Comments

There are no other terms below 2^24.

There are no other terms below 10^8. - Lucas A. Brown, Aug 11 2024

Links

Table of n, a(n) for n=1..5.

Lucas A. Brown, Python program.

Tomohiro Yamada, On a problem of De Koninck, Moscow Journal of Combinatorics and Number Theory, 10:3 (2021), 249-260, correction, 10:4 (2021), 339.

Example

7 is a term since 7^2 + 7 + 1 = 3 * 19, 3^2 + 3 + 1 = 13 and 13 + 1 = 2 * 7.

Prog

(PARI) is(p)={my(W, V1, V2, V3, q1, q2, q3, i1, i2, i3, l1, l2, l3); W=0; V1=factor(p^2+p+1); l1=length(V1[, 1]); for(i1=1, l1, q1=V1[i1, 1]; V2=factor(q1+1); l2=length(V2[, 1]); for(i2=1, l2, q2=V2[i2, 1]; V3=factor(q2^2+q2+1); l3=length(V3[, 1]); for(i3=1, l3, q3=V3[i3, 1]; if(q3==p, W=[p, q1, q2])))); W}

Crossrefs

Cf. A101368, A347988.

Sequence in context: A059406 A042791 A128293 * A307291 A326262 A071409

Adjacent sequences: A354423 A354424 A354425 * A354427 A354428 A354429

Keyword

nonn,more,hard

Author

Tomohiro Yamada, May 27 2022

Status

approved