A392559 Numbers x such that for some y, a divisor of x such that 1<y<x, the following four numbers are prime: x*y+1, x*y-1, x/y+1, x/y-1.

30, 36, 48, 60, 72, 90, 120, 126, 132, 144, 156, 204, 210, 216, 240, 252, 270, 288, 300, 336, 348, 360, 420, 432, 450, 468, 504, 510, 522, 540, 588, 612, 780, 792, 828, 882, 918, 960, 966, 1044, 1050, 1116, 1128, 1140, 1188, 1224, 1260, 1296, 1368, 1386, 1404, 1422

Offset

1,1

Comments

All terms are multiples of 6.

Links

Table of n, a(n) for n=1..52.

Prog

(Python)
from sympy import isprime, divisors
print([x for x in range(2, 2000) if any(all(isprime(v) for v in (x//y-1, x//y+1, x*y-1, x*y+1)) for y in divisors(x)[1:-1])])
(PARI) isok(k) = fordiv(k, d, if ((d>1) && (d<k) && isprime(k*d+1) && isprime(k*d-1) && isprime(k/d+1) && isprime(k/d-1), return(1))); \\ Michel Marcus, Mar 16 2026

Crossrefs

Cf. A000040.

Subsequence of A280270 (both x/y+1 and x*y+1 are prime).

Sequence in context: A345382 A227680 A109426 * A167325 A051657 A257439

Adjacent sequences: A392556 A392557 A392558 * A392560 A392561 A392562

Keyword

nonn

Author

Alex Ratushnyak, Mar 15 2026

Status

approved