OFFSET
1,1
COMMENTS
a(28) > 10^8.
2348273369086 and 79164837199871 are also terms. - Robert Israel, Feb 19 2026
LINKS
Brian Hayes, Does having prime neighbors make you more composite?, Bit-Player Article, Nov 04 2021.
EXAMPLE
k | omega(k)*omega(k + 1)*omega(k + 2)*omega(k + 3)
---------------------------------------------------------------------
9 | 1 * 2 * 1 * 2 = 4
... |
65536 | 1 * 1 * 4 * 1 = 4
131071 | 1 * 1 * 2 * 2 = 4
995326 | 2 * 1 * 2 * 1 = 4
MAPLE
Res:= NULL: count:= 0:
W:= [seq(NumberTheory:-Omega(i, distinct), i=1..4)]:
for k from 2 to 10^6 do
W:= [W[2], W[3], W[4], NumberTheory:-Omega(k+3, distinct)];
if convert(W, `*`)=4 then Res:= Res, k; count:= count+ 1; fi
od:
Res; # Robert Israel, Feb 11 2026
MATHEMATICA
seq[lim_] := Module[{s = {}, om = PrimeNu[Range[2, 5]], i = 1}, Do[If[Times @@ om == 4, AppendTo[s, k - 4]]; om[[i]] = PrimeNu[k]; i = Mod[i, 4] + 1, {k, 6, lim}]; s]; seq[10^6] (* Amiram Eldar, Feb 03 2026 *)
PROG
(Magma) [k: k in [1..10^6] | #PrimeDivisors(k)*#PrimeDivisors(k+1)*#PrimeDivisors(k+2)*#PrimeDivisors(k+3) eq 4];
(PARI) isok(k) = omega(k)*omega(k + 1)*omega(k + 2)*omega(k + 3) == 4; \\ Michel Marcus, Feb 18 2026
(PARI) chk(na, nb) = my(p=prod(k=na, na+3, omega(k))); for (k=na+4, nb, p *= omega(k)/omega(na); na++; if (p==4, print1(na, ", ")); ); \\ Michel Marcus, Feb 18 2026
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Juri-Stepan Gerasimov, Feb 01 2026
STATUS
approved
