A347988 Primes p such that q divides p^2 + p + 1, r divides q^2 + q + 1 and p divides r^2 + r + 1 for some primes q and r.

3, 13, 31, 43, 61, 307, 331, 631, 5233

Offset

1,1

Comments

There are no other terms below 2^24. Clearly, if a prime p is in this sequence, then so are q and r. Taking such prime triples (p, q, r) with p smallest, we have three triples (3, 13, 61), (31, 331, 5233), and (43, 631, 307) below 2^24.

Links

Table of n, a(n) for n=1..9.

Example

3 is a term since 3^2 + 3 + 1 = 13, 13^2 + 13 + 1 = 3 * 61, and 61^2 + 61 + 1 = 3 * 13 * 97.

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(q1^2+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.

Sequence in context: A320587 A077717 A235265 * A275081 A097443 A248368

Adjacent sequences: A347985 A347986 A347987 * A347989 A347990 A347991

Keyword

nonn,hard,more

Author

Tomohiro Yamada, Sep 23 2021

Status

approved