A124936 Numbers k such that k - 1 and k + 1 are semiprimes.

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

Offset

1,1

Comments

All but the first term are even.

Links

Zak Seidov, Table of n, a(n) for n = 1..1000

Formula

a(n) = A092207(n) + 1; at n>=2, a(n) = 2*A082130(n-1).

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
print(list(islice(agen(), 53))) # Michael S. Branicky, Nov 26 2022

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).

Sequence in context: A193325 A303693 A256373 * A213063 A268281 A223137

Adjacent sequences: A124933 A124934 A124935 * A124937 A124938 A124939

Keyword

nonn

Author

Zak Seidov, Nov 13 2006

Status

approved