|
| |
|
|
A320285
|
|
Semiprimes followed by successive gaps 4, 6, 9.
|
|
0
|
|
|
|
8203, 9703, 18163, 35823, 72687, 72847, 75759, 95695, 97959, 132879, 177159, 194127, 198763, 201099, 210379, 223807, 226887, 228043, 299227, 306283, 344779, 347527, 351399, 360763, 403467, 407107, 454143, 487927, 506467, 514927, 516487, 532803, 537367, 538903, 546847, 556707, 562819
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
1,1
|
|
|
COMMENTS
|
4, 6, 9 are the first 3 semiprimes (A001358).
Are there semiprimes followed by gaps {4, 6, 9, 10} = the first 4 semiprimes?
Answer: No, one of them would be divisible by 4. - Giovanni Resta, Oct 23 2018
|
|
|
LINKS
|
Table of n, a(n) for n=1..37.
|
|
|
MATHEMATICA
|
spQ[n_] := Plus @@ Last /@ FactorInteger[n] == 2; Select[ Range[10^6/2] 2 + 1, AllTrue[# + {0, 4, 10, 19}, spQ] && Count[ Range[ #+1, #+18], x_ /; spQ@ x] == 2 &] (* Giovanni Resta, Oct 23 2018 *)
|
|
|
PROG
|
(PARI) next_semiprime(n) = for(x=n, oo, if(bigomega(x)==2, return(x)))
is(n) = if(bigomega(n)!=2, return(0)); my(v=[n, next_semiprime(n+1), next_semiprime(next_semiprime(n+1)+1), next_semiprime(next_semiprime(next_semiprime(n+1)+1)+1)]); v[2]-v[1]==4 && v[3]-v[2]==6 && v[4]-v[3]==9 \\ Felix Fröhlich, Oct 23 2018
|
|
|
CROSSREFS
|
Cf. A001358.
Sequence in context: A168346 A331357 A045060 * A168471 A031844 A210008
Adjacent sequences: A320282 A320283 A320284 * A320286 A320287 A320288
|
|
|
KEYWORD
|
nonn
|
|
|
AUTHOR
|
Zak Seidov, Oct 09 2018
|
|
|
STATUS
|
approved
|
| |
|
|
