|
|
A124936
|
|
Numbers k such that k - 1 and k + 1 are semiprimes.
|
|
19
|
|
|
5, 34, 50, 56, 86, 92, 94, 120, 122, 142, 144, 160, 184, 186, 202, 204, 214, 216, 218, 220, 236, 248, 266, 288, 290, 300, 302, 304, 320, 322, 328, 340, 392, 394, 412, 414, 416, 446, 452, 470, 472, 516, 518, 528, 534, 536, 544, 552, 580, 582, 590, 634, 668
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
1,1
|
|
COMMENTS
|
All but the first term are even.
|
|
LINKS
|
|
|
FORMULA
|
|
|
MATHEMATICA
|
lst={}; Do[If[Plus@@Last/@FactorInteger[n-1]==2&&Plus@@Last/@FactorInteger[n+1]==2, AppendTo[lst, n]], {n, 7!}]; lst (* Vladimir Joseph Stephan Orlovsky, Feb 01 2009 *)
Select[Range[2, 700], PrimeOmega[# + 1] == PrimeOmega[# - 1] == 2 &] (* Vincenzo Librandi, Mar 30 2015 *)
|
|
PROG
|
(Magma) IsSemiprime:=func< n | &+[k[2]: k in Factorization(n)] eq 2 >; [ n: n in [1..700] | IsSemiprime(n+1) and IsSemiprime(n-1)]; // Vincenzo Librandi, Mar 30 2015
(PARI) list(lim)=if(lim<5, return([])); my(v=List([5]), x=1, y=1); forfactored(z=7, lim\1+1, if(vecsum(z[2][, 2])==2 && vecsum(x[2][, 2])==2, listput(v, z[1]-1)); x=y; y=z); Vec(v) \\ Charles R Greathouse IV, May 22 2018
(Python)
from sympy import factorint
from itertools import count, islice
def agen(): # generator of terms
yield 5
nxt = 0
for k in count(6, 2):
prv, nxt = nxt, sum(factorint(k+1).values())
if prv == nxt == 2: yield k
|
|
CROSSREFS
|
Cf. A092207 (k and k+2 are semiprimes), A086005 (k-1, k, k+1 are semiprimes), A086006 (primes p such that 2*p-1 and 2*p+1 are semiprimes), A082130 (2*k-1 and 2*k+1 are semiprimes).
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|