A328525 Numbers k such that (k-1)*k*(k+1) = (k-1)*(1+u) = k*(1+v) = (k+1)*(1+w) with primes u, v, w.

3, 5, 9, 21, 55, 131, 145, 155, 231, 259, 265, 449, 495, 561, 595, 1045, 1051, 1365, 1409, 1491, 1549, 1849, 1989, 2001, 2101, 2469, 2785, 3365, 3621, 3641, 3669, 3845, 3911, 4285, 4951, 5181, 5465, 6049, 6699, 7189, 7229, 8219, 8629, 9175, 9521, 9539, 9631, 9729

Offset

1,1

Links

Alois P. Heinz, Table of n, a(n) for n = 1..10000

Example

3 is a term because 2*3*4 = 2*(1+11) = 3*(1+7) = 4*(1+5) with primes 11, 7, 5.
9 is a term because 8*9*10 = 8*(1+89) = 9*(1+79) = 10*(1+71) with primes 89, 79, 71.

Maple

q:= k-> andmap(isprime, (t-> [t-1, t-k, t+k])(k^2-1)):
select(q, [$1..10000])[];  # Alois P. Heinz, Feb 25 2020

Mathematica

Select[Range[2, 10^4], AllTrue[{(# - 1)*#, #*(# + 1), (# + 1)*(# - 1)} - 1, PrimeQ] &] (* Amiram Eldar, Feb 24 2020 *)

Prog

(Rexx)
S = 3
do N = 5 to 595 by 2
   if NOPRIME( N*N +N -1 ) then  iterate N
   if NOPRIME( N*N    -2 ) then  iterate N
   if NOPRIME( N*N -N -1 ) then  iterate N
   S = S || ', ' N
end N
say S
(PARI) isok(k) = isprime(k*(k+1)-1) && isprime((k+1)*(k-1)-1) && isprime(k*(k-1)-1); \\ Michel Marcus, Feb 25 2020

Crossrefs

Cf. A000040.

Intersection of A002328, A028870 and A045546.

Sequence in context: A136401 A147758 A129787 * A125517 A147038 A146275

Adjacent sequences: A328522 A328523 A328524 * A328526 A328527 A328528

Keyword

nonn

Author

Frank Ellermann, Feb 24 2020

Extensions

More terms from Amiram Eldar, Feb 24 2020

Status

approved