A070552 Semiprimes k such that k+1 is also a semiprime.

9, 14, 21, 25, 33, 34, 38, 57, 85, 86, 93, 94, 118, 121, 122, 133, 141, 142, 145, 158, 177, 201, 202, 205, 213, 214, 217, 218, 253, 298, 301, 302, 326, 334, 361, 381, 393, 394, 445, 446, 453, 481, 501, 514, 526, 537, 542, 553, 565, 622, 633, 634, 694, 697

Offset: 1

Author

Sharon Sela (sharonsela(AT)hotmail.com), May 03 2002

Keywords

• nonn

Comments

A064911(a(n))*A064911(a(n)+1) = 1. - Reinhard Zumkeller, Dec 03 2009

Links

• D. W. Wilson, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A001358, A007674, A039832, A100484.

Programs

Magma

IsSemiprime:=func< n | &+[k[2]: k in Factorization(n)] eq 2 >; [ n: n in [4..700] | IsSemiprime(n) and IsSemiprime(n+1) ]; // Vincenzo Librandi, Jan 22 2016

Mathematica

f[n_]:=Last/@FactorInteger[n]=={1,1}||Last/@FactorInteger[n]=={2};lst={};Do[If[f[n]&&f[n+1],AppendTo[lst,n]],{n,7!}];lst (* Vladimir Joseph Stephan Orlovsky, Feb 25 2010 *)
Flatten[Position[Partition[Table[If[PrimeOmega[n]==2,1,0],{n,700}],2,1],{1,1}]] (* Harvey P. Dale, Feb 04 2015 *)
Select[Range[700], PrimeOmega[#] == PrimeOmega[# + 1] == 2 &] (* Vincenzo Librandi, Jan 22 2016 *)

PARI

forprime(p=3,1e3,if(bigomega(2*p-1)==2,print1(2*p-1", "));if(bigomega(2*p+1)==2,print1(2*p", "))) \\ Charles R Greathouse IV, Nov 09 2011

PARI

is(n)=if(n%2, isprime((n+1)/2) && bigomega(n)==2, isprime(n/2) && bigomega(n+1)==2) \\ Charles R Greathouse IV, Sep 08 2015

Python

from sympy import factorint
def is_semiprime(n): return sum(e for e in factorint(n).values()) == 2
def ok(n): return is_semiprime(n) and is_semiprime(n+1)
print(list(filter(ok, range(698)))) # Michael S. Branicky, Sep 14 2021

Formula

a(n) >> n log n since either n or n+1 is in A100484. - Charles R Greathouse IV, Jul 21 2015

a(n) = A109373(n) - 1. - Zak Seidov Dec 19 2018

Extensions

More terms from Vladeta Jovovic, May 03 2002