A354428
Primes p such that q divides p^2 + p + 1, r divides q + 1 and p divides r^2 + r + 1 for some primes q and r.
Original entry on oeis.org
3, 7, 43, 73363, 1477111
Offset: 1
43 is a term since 43^2 + 43 + 1 = 3 * 631, 631 + 1 = 2^3 * 79, and 79^2 + 79 + 1 = 3 * 7^2 * 43.
Cf.
A354426 (r corresponding to primes p in this sequence),
A354427 (q corresponding to primes p in this sequence).
-
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}
A357870
Triangle of integers related to generalized Markov numbers, read by rows.
Original entry on oeis.org
3, 13, 51, 61, 217, 846, 291, 1001, 3673, 14637, 1393, 4683, 16693, 62221, 247965, 6673, 22265, 77064, 282317, 1054081, 4200768, 31971, 106153, 360517, 1285131, 4778353, 17857153, 71165091
Offset: 1
Triangle begins:
3;
13, 51;
61, 217, 846;
291, 1001, 3673, 14637;
1393, 4683, 16693, 62221, 247965;
...
A355298
Primes p such that q divides p + 1, r divides q^2 + q + 1, s divides r^2 + r + 1, and p divides s^2 + s + 1 for some primes q, r, and s.
Original entry on oeis.org
3, 13, 61, 127, 399403
Offset: 1
61 is a term since 61 + 1 = 2 * 31, 31^2 + 31 + 1 = 3 * 331, 3^2 + 3 + 1 = 13, and 13^2 + 13 + 1 = 3 * 61.
-
is(p)={my(W, V1, V2, V3, V4, q1, q2, q3, q4, i1, i2, i3, i4, l1, l2, l3, l4); W=0; V1=factor(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]; V4=factor(q3^2+q3+1); l4=length(V4[, 1]); for(i4=1, l4, q4=V4[i4, 1];if(q4==p, W=[p, q1, q2, q3]))))); W}
Comments