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.
Do[ f = 21^n - 2; If[ PrimeQ[ f ], Print[ {n, f} ] ], {n,1,1000} ]
[n: n in [1..1000]| IsPrime(7^n-6)]
A191469:=n->`if`(isprime(7^n-6),n,NULL): seq(A191469(n), n=1..10^3); # Wesley Ivan Hurt, Nov 14 2014
Select[Range[1,5000],PrimeQ[7^#-6]&] (* Vincenzo Librandi, Aug 05 2012 *)
for(n=1, 10^6, if(isprime(7^n-6), print1(n, ", ")))
For p = 79, the next prime number is 83. The numbers between 79 and 83 and the prime divisors are respectively 80 { 2, 5 }, 81 { 3 }, 82 { 2, 41 }. The set of prime divisors is { 2, 3, 5, 41 } and has 4 elements, so 79 is a term. - _Marius A. Burtea_, Sep 26 2019
a:=[]; for p in PrimesInInterval(2,4800) do b:={}; for s in [p..NextPrime(p)-1] do if not IsPrime(s) then b:=b join Set(PrimeDivisors(s)); end if; end for; if #Set(b) eq 4 then Append(~a,p); end if; end for; a; // Marius A. Burtea, Sep 26 2019
Select[Prime@ Range@ 650, Length@ Union@ Flatten@ Map[First /@ FactorInteger@ # &, Select[Range[#, NextPrime@ #], CompositeQ]] == 4 &] (* Michael De Vlieger, May 27 2016 *) Join[{13,79},Select[Prime[Range[23,650]],PrimeQ[#+2]&&PrimeNu[#+1]==4&]] (* This program assumes the correctness of the conjecture by Charles R. Greathouse, IV, in the Comments. *) (* Harvey P. Dale, Jun 07 2019 *)
lista(nn)=forprime(p=2, nn, allp = []; forcomposite (c = p+1, nextprime(p+1), allp = Set(concat(allp, (factor(c)[,1])~));); if (#allp == 4, print1(p, ", "));); \\ Michel Marcus, May 28 2016
is(n)=if(!isprime(n), return(0)); if(isprime(n+2), return(omega(n+1)==4)); if(isprime(n+4), omega(n+1)+omega(n+2)+omega(n+3)==5, 0) list(lim)=my(v=List(),t,p); lim\=1; for(e=4,logint(lim+2,3), p=precprime(3^e); if(isprime(p+4) && is(p), listput(v,p))); for(e=4,logint(lim+3,2), p=precprime(2^e); if(isprime(p+4) && is(p), listput(v,p))); p=2; forprime(q=3,lim+2, if(q-p==2 && omega(p+1)==4, listput(v,p)); p=q); Set(v) \\ Charles R Greathouse IV, Jun 01 2016
[7^n-6: n in [1..30]]; // Vincenzo Librandi, Feb 06 2013
CoefficientList[Series[(1 + 35 x)/((1-x) (1-7 x)), {x, 0, 30}], x] (* Vincenzo Librandi, Feb 06 2013 *)
NestList[7 # + 36 & , 1, 18] (* Bruno Berselli, Feb 06 2013 *)
LinearRecurrence[{8,-7},{1,43},30] (* Harvey P. Dale, Nov 27 2014 *)
a(n)=7^n-6 \\ Charles R Greathouse IV, Oct 07 2015
a(1) = 3 because 3^3-2 = 25 = 5*5. a(2) = 8 because 3^8-2 = 6559 = 7*937. a(3) = 10 because 3^10-2 = 59047 = 137*431.
Do[f = 3^n - 2; If[ !PrimeQ[f], s = FactorIntegerECM[f]; If[PrimeQ[s] && PrimeQ[f/s], Print[n]]], {n, 2, 10^3}] (* Ryan Propper, May 11 2007 *)
for(n=1,200,if(bigomega(3^n-2)==2,print1(n","))) /* Herman Jamke (hermanjamke(AT)fastmail.fm), Apr 02 2007 */
a(1) = 4 because 4^1 - 2 = 2 is prime, a(3) = 9 because 3^3 - 2 = 25, 5^3 - 2 = 123 and 7^3 - 2 = 341 = 11 * 31 are composite, whereas 9^3 - 2 = 727 is prime.
f:= proc(n) local k;
for k from 3 by 2 do
if isprime(k^n-2) then return k fi
od
end proc:
f(1):= 4: f(2):= 2:
map(f, [$1..100]); # Robert Israel, Jul 15 2018
a095303[n_] := For[k = 1, True, k++, If[PrimeQ[k^n - 2], Return[k]]]; Array[a095303, 100] (* Jean-François Alcover, Mar 01 2019 *)
for (n=1,73,for(k=1,oo,if(isprime(k^n-2),print1(k,", ");break))) \\ Hugo Pfoertner, Oct 28 2018
[Max(PrimeDivisors(3^n-2)):n in [2..30]]; // Marius A. Burtea, Jul 12 2019
FactorInteger[#][[-1,1]]&/@(3^Range[2,30]-2) (* Harvey P. Dale, Apr 07 2022 *)
a(n) = vecmax(factor(3^n-2)[,1]); \\ Michel Marcus, Jul 12 2019
f[n_]:=3^n-2; lst={};Do[p=Prime[n];If[PrimeQ[f[p]],Print[p];AppendTo[lst,p]],{n,7!}];lst (* Vladimir Joseph Stephan Orlovsky, Jul 17 2009 *)
[11^n - 2: n in [1..50]]; // Vincenzo Librandi, Jun 08 2011
LinearRecurrence[{12, -11},{9, 119},17] (* Ray Chandler, Aug 26 2015 *)
a(1) = 11^4 - 2 = 14639, a(2) = 11^6 - 2 = 1771559.
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