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 1-8 of 8 results.

A252788 Numbers m such that 3^m + m is a semiprime.

Original entry on oeis.org

1, 4, 7, 14, 16, 20, 22, 32, 38, 55, 80, 92, 188, 220, 296, 328, 370, 422, 452, 454, 500, 650, 934, 962
Offset: 1

Views

Author

Vincenzo Librandi, Dec 22 2014

Keywords

Comments

a(21) >= 500. - Hugo Pfoertner, Aug 03 2019
From Kevin P. Thompson, Apr 24 2022: (Start)
a(25) >= 1402.
m=1448 is also a term of this sequence. (End)

Examples

			1 is in this sequence because 3^1+1 = 2*2 is semiprime.
14 is in this sequence because 3^14+14 = 283*16901 and these two factors are prime.

Links

Crossrefs

Cf. numbers m such that k^m+m is a semiprime: A085745 (k=2), this sequence (k=3), A252789 (k=4), A252790 (k=5), A252791 (k=6), A252792 (k=7), A252793 (k=8), A252794 (k=9), A252795 (k=10).
Cf. A252656.

Programs

  • Magma
    IsSemiprime:=func; [m: m in [1..130] | IsSemiprime(s) where s is 3^m+m];
  • Mathematica
    Select[Range[130], PrimeOmega[3^# + #]==2 &]
  • PARI
    first(m)=my(v=vector(m),r=1);for(i=1,m,while(bigomega(3^r + r)!=2,r++);v[i]=r;r++);v; \\ Anders Hellström, Aug 14 2015

Extensions

a(13)-a(16) from Luke March, Jul 18 2015
a(17)-a(20) from Carl Schildkraut, Aug 19 2015
a(21)-a(24) from Kevin P. Thompson, Apr 24 2022

A252657 Numbers m such that 4^m - m is a semiprime.

Original entry on oeis.org

2, 11, 17, 33, 55, 59, 63, 153, 315
Offset: 1

Views

Author

Vincenzo Librandi, Dec 20 2014

Keywords

Comments

549, 721, and 755 are in the sequence, but not necessarily the next three terms. The other possibilities for a(9) are 483, 503, and 543. - Robert Israel, Feb 10 2019

Examples

			2 is in this sequence because 4^2-2 = 2*7 is semiprime.
17 is in this sequence because 4^17-17 = 6971*2464477 and these two factors are prime.

Links

Crossrefs

Cf. A024037 (4^n - n).
Cf. similar sequences listed in A252656.

Programs

  • Magma
    IsSemiprime:=func; [m: m in [2..120] | IsSemiprime(s) where s is 4^m-m];
  • Mathematica
    Select[Range[120], PrimeOmega[4^# - #]==2 &]

Extensions

a(8)-a(9) from Luke March, Jul 08 2015

A252658 Numbers m such that 5^m - m is a semiprime.

Original entry on oeis.org

1, 3, 8, 14, 18, 48, 52, 54, 62, 72, 96, 98, 114, 186, 486, 524, 712
Offset: 1

Views

Author

Vincenzo Librandi, Dec 20 2014

Keywords

Comments

There are no other known terms under 1000 - the only possible terms are 812 and 908. - Carl Schildkraut, Aug 21 2015

Examples

			1 is in this sequence because 5^1-1 = 2*2 is semiprime.
18 is in this sequence because 5^18-18 = 199*19169332993 and these two factors are prime.

Crossrefs

Cf. similar sequences listed in A252656.

Programs

  • Magma
    IsSemiprime:=func; [m: m in [1..100] | IsSemiprime(s) where s is 5^m-m];
  • Mathematica
    Select[Range[100], PrimeOmega[5^# - #]==2 &]
  • PARI
    isok(n)=bigomega(5^n - n)==2 \\ Anders Hellström, Aug 21 2015

Extensions

a(13)-a(17) from Carl Schildkraut, Aug 21 2015

A252659 Numbers m such that 6^m - m is a semiprime.

Original entry on oeis.org

2, 3, 5, 10, 15, 23, 34, 37, 47, 70, 259, 275, 278, 497, 563
Offset: 1

Views

Author

Vincenzo Librandi, Dec 21 2014

Keywords

Comments

From Robert Israel, Sep 06 2016: (Start)
Even n is in this sequence iff (6^n-n)/2 is prime.
3*k is in this sequence iff 2*6^(3*k-1)-k is prime.
Also contains 275, 278 and 683.
The only other possible member less than 275 is 259. (End)
a(16) >= 617. - Kevin P. Thompson, Apr 29 2022

Examples

			2 is in this sequence because 6^2-2 = 2*17 is semiprime.
10 is in this sequence because 6^10-10 = 2*30233083 and these two factors are prime.

Links

Crossrefs

Cf. similar sequences listed in A252656.

Programs

  • Magma
    IsSemiprime:=func; [m: m in [1..90] | IsSemiprime(s) where s is 6^m-m];
  • Maple
    Res:= NULL:
for n from 1 to 100 do
    F:= ifactors(6^n-n, easy)[2];
    if add(t[2], t=F) >= 3 or (hastype(F, symbol) and add(t[2], t=F) >= 2)
       then flag:= false
    elif add(t[2], t=F) = 2 and not hastype(F, symbol) then flag:= true
    else
     flag:= evalb(numtheory:-bigomega(6^n-n)=2)
    fi;
  if flag then  Res:= Res, n fi
od:
Res; # Robert Israel, Sep 06 2016
  • Mathematica
    Select[Range[90], PrimeOmega[6^# - #]== 2&]

Extensions

a(11)-a(15) from Kevin P. Thompson, Apr 29 2022

A252660 Numbers k such that 7^k - k is a semiprime.

Original entry on oeis.org

1, 20, 26, 32, 54, 162, 204
Offset: 1

Views

Author

Vincenzo Librandi, Dec 21 2014

Keywords

Comments

From Robert Israel, Sep 02 2016: (Start)
Odd k is in the sequence iff (7^k-k)/2 is prime.
If k == 1 (mod 3) then k is in the sequence iff (7^k-k)/3 is prime.
708 is in the sequence but is not necessarily a(7). (End)
a(8) >= 384. - Daniel Suteu, Aug 05 2019

Examples

			1 is in this sequence because 7^1-1 = 2*3 is semiprime.
20 is in this sequence because 7^20-20 = 1511201*52800564781 and these two factors are prime.

Crossrefs

Cf. similar sequences listed in A252656.

Programs

  • Magma
    IsSemiprime:=func; [m: m in [1..80] | IsSemiprime(s) where s is 7^m-m];
  • Maple
    Res:= NULL:
for n from 1 to 100 do
      F:= ifactors(7^n-n,easy)[2];
    if add(t[2],t=F) >= 3 or (hastype(F,symbol) and add(t[2],t=F) >= 2)
       then flag:= false
    elif add(t[2],t=F) = 2 and not hastype(F,symbol) then flag:= true
    else
      flag:= evalb(numtheory:-bigomega(7^n-n)=2)
    fi;
  if flag then  Res:= Res, n fi
od:
Res; # Robert Israel, Sep 02 2016
  • Mathematica
    Select[Range[80], PrimeOmega[7^# - #]==2 &]

Extensions

a(6) from Robert Israel, Sep 02 2016
a(7) from Daniel Suteu, Aug 05 2019

A252661 Numbers m such that 8^m - m is a semiprime.

Original entry on oeis.org

2, 7, 9, 111, 129, 133, 361
Offset: 1

Views

Author

Vincenzo Librandi, Dec 21 2014

Keywords

Comments

a(8) >= 369. - Hugo Pfoertner, Aug 03 2019

Examples

			2 is in this sequence because 8^2-2 = 2*31 is semiprime.
9 is in this sequence because 8^9-9 = 23*5835553 and these two factors are prime.

Links

Crossrefs

Cf. similar sequences listed in A252656.

Programs

  • Magma
    IsSemiprime:=func; [m: m in [1..70] | IsSemiprime(s) where s is 8^m-m];
  • Mathematica
    Select[Range[70],PrimeOmega[8^# - #]==2 &]

Extensions

a(4)-a(7) from Hugo Pfoertner, Aug 03 2019

A252662 Numbers m such that 9^m - m is a semiprime.

Original entry on oeis.org

4, 8, 10, 14, 20, 26, 38, 44, 56, 80, 190
Offset: 1

Views

Author

Vincenzo Librandi, Dec 22 2014

Keywords

Comments

a(12) >= 250. - Hugo Pfoertner, Aug 03 2019

Examples

			4 is in this sequence because 9^4-4 = 79*83 and these two factors are prime.
14 is in this sequence because 9^14-14 = 163*140348419969 and these two factors are prime.

Links

Crossrefs

Cf. similar sequences listed in A252656.

Programs

  • Magma
    IsSemiprime:=func; [m: m in [1..80] | IsSemiprime(s) where s is 9^m-m];
  • Mathematica
    Select[Range[80], PrimeOmega[9^# - #]==2 &]

Extensions

a(11) from Hugo Pfoertner, Aug 03 2019

A252663 Numbers m such that 10^m - m is a semiprime.

Original entry on oeis.org

1, 7, 9, 11, 15, 33, 77, 93, 107, 117, 143, 149, 177, 209, 221
Offset: 1

Views

Author

Vincenzo Librandi, Dec 22 2014

Keywords

Comments

a(16) >= 269. - Hugo Pfoertner, Aug 04 2019

Examples

			1 is in this sequence because 10^1-1 = 3*3 is semiprime.
9 is in this sequence because 10^9-9 = 67*14925373 and these two factors are prime.

Links

Crossrefs

Cf. similar sequences listed in A252656.

Programs

  • Magma
    IsSemiprime:=func; [m: m in [1..80] | IsSemiprime(s) where s is 10^m-m];
  • Mathematica
    Select[Range[80], PrimeOmega[10^# - #]==2 &]
  • PARI
    is(m) = bigomega(10^m - m) == 2; \\ Jinyuan Wang, Jul 09 2019

Extensions

a(8) from Luke March, Jul 08 2015
a(9)-a(13) from Daniel Suteu, Jul 09 2019
a(14), a(15) from Hugo Pfoertner, Aug 04 2019
Showing 1-8 of 8 results.

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