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 1-2 of 2 results.

A252656 Numbers n such that 3^n - n is a semiprime.

Original entry on oeis.org

4, 6, 10, 25, 28, 32, 98, 124, 146, 164, 182, 190, 200, 220, 226, 230, 248, 280, 362, 376, 418, 446, 518, 544
Offset: 1

Views

Author

Vincenzo Librandi, Dec 20 2014

Keywords

Comments

Are there odd members of the sequence other than 25? There are no others < 10000. An odd number m is in the sequence iff (3^m - m)/2 is prime. - Robert Israel, Jan 02 2015
No more odd terms after a(4) = 25 for m < 200000. a(25) >= 626. - Hugo Pfoertner, Aug 07 2019

Examples

			4 is in this sequence because 3^4 - 4 = 7*11 is semiprime.
10 is in this sequence because 3^10 - 10 = 43*1373 and these two factors are prime.

Links

Crossrefs

Cf. numbers m such that k^m - m is a semiprime: A165767 (k = 2), this sequence (k = 3), A252657 (k = 4), A252658 (k = 5), A252659 (k = 6), A252660 (k = 7), A252661 (k = 8), A252662 (k = 9), A252663 (k = 10).
Cf. A001358 (semiprimes), A058037, A252788.

Programs

  • Magma
    IsSemiprime:=func; [m: m in [2..150] | IsSemiprime(s) where s is 3^m-m];
  • Maple
    select(n -> numtheory:-bigomega(3^n - n) = 2, [$1..150]); # Robert Israel, Jan 02 2015
  • Mathematica
    Select[Range[150], PrimeOmega[3^# - #] == 2 &]
  • PARI
    is(m) = bigomega(3^m-m)==2 \\ Felix Fröhlich, Dec 30 2014
  • PARI
    n=1;while(n<100,s=3^n-n;c=0;forprime(p=1,10^4,if(s%p,c++);if(s%p==0,s1=s/p;if(ispseudoprime(s1),print1(n,", ");c=0;break);if(!ispseudoprime(s1),c=0;break)));if(!c,n++);if(c,if(bigomega(s)==2,print1(n,", "));n++)) \\ Derek Orr, Jan 02 2015

Extensions

a(10) from Felix Fröhlich, Dec 30 2014
a(11)-a(14) from Charles R Greathouse IV, Jan 02 2015
a(15)-a(24) from Luke March, Aug 21 2015

A252789 Numbers m such that 4^m + m is a semiprime.

Original entry on oeis.org

7, 19, 39, 43, 87, 135, 147, 177, 223, 255, 403
Offset: 1

Views

Author

Vincenzo Librandi, Dec 24 2014

Keywords

Comments

From Kevin P. Thompson, Apr 26 2022: (Start)
a(12) >= 765.
795 and 949 are also terms in this sequence. (End)

Examples

			7 is in this sequence because 4^7+7 = 37*443 and these two factors are prime.
19 is in this sequence because 4^19+19 = 11*24988900633 and these two factors are prime.

Links

Crossrefs

Cf. similar sequences listed in A252788.
Cf. A252657.

Programs

  • Magma
    IsSemiprime:=func; [m: m in [1..130] | IsSemiprime(s) where s is 4^m+m];
  • Mathematica
    Select[Range[130], PrimeOmega[4^# + #]==2 &]
  • PARI
    main(m)=select(m->bigomega(4^m + m)==2, vector(m, i, i)); \\ Anders Hellström, Aug 14 2015

Extensions

a(6)-a(9) from Carl Schildkraut, Aug 14 2015
a(10)-a(11) from Kevin P. Thompson, Apr 26 2022
Showing 1-2 of 2 results.

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