cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-4 of 4 results.

A175680 Semiprimes that are not Chen semiprimes A175634.

Original entry on oeis.org

4, 14, 26, 38, 46, 62, 74, 77, 86, 94, 95, 106, 121, 122, 134, 143, 146, 158, 161, 166, 178, 185, 194, 203, 206, 218, 221, 226, 254, 262, 278, 302, 314, 321, 326, 329, 334, 339, 341, 346, 362, 365, 371, 381, 386, 395, 398, 422, 437, 446, 451, 458, 466, 471
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Aug 08 2010

Keywords

Comments

Non-Chen semiprimes: semiprimes m such that m+4 is neither a prime or a semiprime.

Programs

  • Python
    from sympy.ntheory.factor_ import primeomega, isprime
def issemiprime(n): return primeomega(n) == 2
def ok(n): return issemiprime(n) and not (issemiprime(n+4) or isprime(n+4))
print(list(filter(ok, range(1, 472)))) # Michael S. Branicky, Apr 14 2021

Extensions

Corrected (234 replaced by 254, 471 inserted) by R. J. Mathar, Aug 10 2010

A175735 n-th non-Chen semiprime minus n-th Chen semiprime.

Original entry on oeis.org

-2, 5, 16, 23, 25, 40, 49, 44, 52, 59, 56, 57, 70, 67, 77, 85, 81, 89, 79, 81, 91, 94, 101, 92, 91, 100, 102, 103, 125, 129, 137, 160, 169, 166, 167, 160, 157, 156, 154, 145, 160, 160, 162, 168, 172, 180, 181, 203, 202, 209, 204, 209, 213, 212, 208, 215, 228, 227, 237, 236
Offset: 1

Views

Author

Juri-Stepan Gerasimov, Aug 25 2010

Keywords

Comments

Chen semiprimes: semiprimes m such that m+4 is either a prime or a semiprime.

Programs

  • Maple
    isA175634 := proc(n) isA001358(n) and (isprime(n+4) or isA001358(n+4)) ; end proc:
A175634 := proc(n) option remember; if n = 1 then 6; else for a from procname(n-1)+1 do if isA175634(a) then return a; end if; end do: end if; end proc:
isA175680 := proc(n) isA001358(n) and not isA175634(n) ; end proc:
A175680 := proc(n) option remember; if n = 1 then 4; else for a from procname(n-1)+1 do if isA175680(a) then return a; end if; end do: end if; end proc:
A175735 := proc(n) A175680(n)-A175634(n) ; end proc:
seq(A175735(n),n=1..120) ; # R. J. Mathar, Aug 25 2010

Formula

a(n) = A175680(n) - A175634(n).

Extensions

Keyword:sign,less set; corrected (87 replaced by 91, 210 replaced by 204) - R. J. Mathar, Aug 25 2010. Also corrected by D. S. McNeil, Aug 25 2010

A211410 Chen triprimes, triprimes (A014612) m such that m+2 is either prime or semiprime.

Original entry on oeis.org

8, 12, 20, 27, 44, 45, 63, 75, 92, 99, 105, 116, 117, 125, 147, 153, 164, 165, 171, 175, 195, 207, 212, 231, 245, 255, 261, 275, 279, 285, 325, 332, 333, 345, 356, 357, 363, 369, 387, 399, 425, 429, 435, 452, 455, 465, 477, 483, 507, 524
Offset: 1

Views

Author

Jonathan Vos Post, Feb 09 2013

Keywords

Examples

			27=3^3 and 45=3^2*9 are in the sequence because 27+2 = 29 and 45+2 = 47 are primes.
8=2^3, 12=2^2*3, and 20=2^2*5 are in the sequence because 8+2=10=2*5, 12+2=14=2*7, and 20+2=22=2*11 are semiprimes (A001358).

Links

Crossrefs

Cf. A001358, A014612, A109611, A175634.

Programs

  • Maple
    A211410 := proc(n)
    option remember;
    local a;
    if n = 1 then
        8;
    else
        for a from procname(n-1)+1 do
            if numtheory[bigomega](a) = 3 then
                if isprime(a+2) or numtheory[bigomega](a+2) = 2 then
                    return a;
                end if;
            end if;
        end do:
    end if;
end proc:
seq(A211410(n),n=1..80) ; # R. J. Mathar, Feb 10 2013
  • Mathematica
    Select[Range[600],PrimeOmega[#]==3&&PrimeOmega[#+2]<3&] (* Harvey P. Dale, Jul 15 2019 *)
  • PARI
    issemi(n)=bigomega(n)==2
list(lim)=my(v=List(),pq); forprime(p=2,lim\4, forprime(q=2,min(lim\2\p,p), pq=p*q; forprime(r=2,min(lim\pq,q), if(isprime(pq*r+2) || issemi(pq*r+2), listput(v,pq*r))))); Set(v) \\ Charles R Greathouse IV, Aug 23 2017

A221865 The nonprimes k such that k + 2 is either a prime or a semiprime.

Original entry on oeis.org

0, 1, 4, 8, 9, 12, 15, 20, 21, 24, 27, 32, 33, 35, 36, 39, 44, 45, 49, 51, 55, 56, 57, 60, 63, 65, 69, 72, 75, 77, 80, 81, 84, 85, 87, 91, 92, 93, 95, 99, 104, 105, 111, 116, 117, 119, 120, 121, 125, 129, 132, 135, 140, 141, 143, 144, 147, 153, 155, 156, 159, 161, 164, 165, 171, 175, 176, 177, 183
Offset: 1

Views

Author

Gerasimov Sergey, Apr 18 2013

Keywords

Comments

Chen primes A109611(n) such that A109611(n)-/+ a(n) are both prime: 2, 29, 53, 113, 139,...
Unrelated: Numbers n such that n + 2^bigomega(n) is either a prime or a semiprime: 1, 2, 3, 5, 6, 7, 9, 10, 11, 13, 15, 17, 18, 19, 21, 22, 23, 25, 27,...
A179384 is a subsequence. - R. J. Mathar, Apr 26 2013

Crossrefs

Cf. A001358, A109611, A175634.

Programs

  • Maple
    A221865 := proc(n)
    option remember;
    if n =1 then
        0;
    else
        for a from procname(n-1)+1 do
            if not isprime(a) then
            if isprime(a+2) or numtheory[bigomega](a+2) = 2 then
                return a;
            end if;
            end if;
        end do:
    end if;
end proc: # R. J. Mathar, Apr 26 2013
  • Mathematica
    Select[Range[0,200],!PrimeQ[#]&&PrimeOmega[#+2]<3&] (* Harvey P. Dale, May 05 2013 *)

Extensions

Corrected by R. J. Mathar, Apr 26 2013
Showing 1-4 of 4 results.

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