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

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

Offset: 1

Author

Vincenzo Librandi, Dec 21 2014

Keywords

• nonn
• more

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