A268209
Numbers n of the form 2^k + 1 such that n - k is a prime q (for k >= 0).
Original entry on oeis.org
2, 3, 5, 17, 65, 65537, 262145, 18014398509481985, 288230376151711745, 1267650600228229401496703205377, 1329227995784915872903807060280344577
Offset: 1
17 = 2^4 + 1 is a term because 17 - 4 = 13 (prime).
257 = 2^8 + 1 is not a term because 257 - 8 = 249 (composite number).
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[2^k + 1: k in [0..60] | IsPrime(2^k - k + 1)]
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2^# + 1 &@ Select[Range[0, 600], PrimeQ[2^# - # + 1] &] (* Michael De Vlieger, Jan 29 2016 *)
A268210
Primes p of the form 2^k + 1 such that p - k is a prime q (for k >= 0).
Original entry on oeis.org
2, 3, 5, 17, 65537
Offset: 1
Prime 17 = 2^4 + 1 is a term because 17 - 4 = 13 (prime).
257 = 2^8 + 1 is not a term because 257 - 8 = 249 (composite number).
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[2^k + 1: k in [0..60] | IsPrime(2^k + 1) and IsPrime(2^k - k + 1)];
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2^# + 1 &@ Select[Range[0, 600], PrimeQ[2^# + 1] && PrimeQ[2^# - # + 1] &] (* Michael De Vlieger, Jan 29 2016 *)
A239323
Semiprimes of the form (2^n + 1)*(2^n - n + 1).
Original entry on oeis.org
4, 6, 15, 221, 4294049777
Offset: 1
4 is in this sequence because (2^0 + 1)*(2^0 - 0 + 1) = 2*2 = 4 is semiprime for n = 0,
6 is in this sequence because (2^1 + 1)*(2^1 - 1 + 1) = 3*2 = 6 is semiprime for n = 1,
15 is in this sequence because (2^2 + 1)*(2^2 - 2 + 1) = 5*3 = 15 is semiprime for n = 2.
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k := 1;
for n in [1..10000] do
if IsPrime(k*2^n + 1) and IsPrime(k*2^n - n + 1) then
(k*2^n + 1)*(k*2^n - n + 1);
end if;
end for;
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Select[Table[(2^n+1)(2^n-n+1),{n,0,20}],PrimeOmega[#]==2&] (* Harvey P. Dale, May 11 2024 *)
A246516
Primes of the form 2*4^n - n.
Original entry on oeis.org
2, 7, 549755813869, 2475880078570760549798248403
Offset: 1
2*4^0 - 0 = 2 is prime, thus 2 is a member of this sequence.
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[a: n in [0..500] | IsPrime(a) where a is 2*4^n - n];
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Select[Table[2^(2n + 1) - n, {n, 0, 127}], PrimeQ] (* Alonso del Arte, Sep 16 2014 *)
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for(n=0,10^3,if(ispseudoprime(2^(2*n+1)-n),print1(2^(2*n+1)-n,", "))) \\ Derek Orr, Aug 28 2014
A308829
Numbers k such that 3^k - k + 1 is prime.
Original entry on oeis.org
0, 1, 5, 27, 45, 47, 75, 8895, 11405, 29517, 84615, 218307
Offset: 1
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ListA[k_] := Block[{seq = {}, n = 0, i = 0}, While[Length[seq] < k, {n = 3^i - i + 1, If[PrimeQ[n], AppendTo[seq, i]], i += 1}]; seq]
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isok(k) = isprime(3^k - k + 1); \\ Jinyuan Wang, Aug 03 2019
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def list_a(k):
return [i for i in range(k) if (3**i) - i + 1 in Primes()]
Showing 1-5 of 5 results.
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