A129613
a(n) is the smallest natural number m such that 2^(2^k) + m is prime for k=0,1,...,n.
Original entry on oeis.org
1, 1, 1, 1, 1, 15, 66747, 475425, 12124167, 14899339905, 8073774344085
Offset: 0
A070694
Numbers b such that b+1, b^2+1, b^4+1, b^8+1 and b^16+1 are primes.
Original entry on oeis.org
1, 2, 337536, 585106, 602056, 2071960, 11861410, 20706120, 54020170, 72696726, 87584646, 89445636, 95895930, 98583340, 98595070, 112204200, 205739220, 279448296, 292582836, 337969690, 349672456, 432972780, 437874186, 474186576, 479631880, 483333426, 621777466, 643697776
Offset: 1
-
Do[ If[ PrimeQ[n + 1] && PrimeQ[n^2 + 1] && PrimeQ[n^4 + 1] && PrimeQ[n^8 + 1] && PrimeQ[n^16 + 1], Print[n]], {n, 1, 10^7}]
Select[Range[21*10^5],AllTrue[#^2^Range[0,4]+1,PrimeQ]&] (* The program generates the first six terms of the sequence. *) (* Harvey P. Dale, Jun 02 2024 *)
A235390
Numbers k such that k^(2^i)+1 are primes for i=0...5.
Original entry on oeis.org
1, 7072833120, 9736020616, 12852419340, 36632235070, 41452651506, 44619665520, 53569833730, 54673378956, 66032908020, 69449109580, 69936419290, 82549220670, 99574135650, 106362659256, 108208833756, 113366066976, 136032409906, 167385272500, 174963279540, 195763339776
Offset: 1
k=7072833120 is in the sequence because the following are six primes: 7072833121, 7072833120^2+1, k^4+1, k^8+1, k^16+1, k^32+1.
A090873
a(n) is the smallest number m such that n^2^k + m^2^k is prime for k=0,1,2,3 and 4.
Original entry on oeis.org
1, 1, 218368, 9324385, 6628674, 601, 365082, 532253, 449140, 4193407, 175746, 2857547, 2752708, 6315245, 80612, 3354745, 10892, 953, 6577504, 157437, 2247676, 11357637, 7650, 272935, 318784, 8034141, 1158380, 22315, 610550, 340357
Offset: 1
a(2)=1 because 2^2^k + 1 is prime for k= 0,1,2,3 and 4.
-
a[n_] := (For[m=1, !(PrimeQ[m+n]&&PrimeQ[m^2+n^2]&&PrimeQ[m^4+n^4]&& PrimeQ[m^8+n^8]&&PrimeQ[m^16+n^16]), m++ ];m);Do[Print[a[n]], {n, 50}]
A335805
Numbers b such that b^(2^i) + 1 is prime for i = 0...6.
Original entry on oeis.org
1, 2072005925466, 5082584069416, 12698082064890, 29990491969260, 46636691707050, 65081025897426, 83689703895606, 83953213480290, 105003537341346, 105699143244090, 107581715369910, 111370557491826, 111587899569066, 128282713771996, 133103004825210
Offset: 1
A337364
Numbers b such that b^(2^i) + 1 is prime for i = 0...7.
Original entry on oeis.org
1, 240164550712338756, 3686834112771042790, 6470860179642426900, 7529068955648085700, 10300630358100537120, 16776829808789151280, 17622040391833711780, 19344979062504927000, 23949099004395080026, 25348938242408650240, 30262840543567048476, 35628481193915651646
Offset: 1
A090874
a(n) is the smallest number m such that m^2^k + (m+1)^2^k is prime for k=0..n.
Original entry on oeis.org
1, 1, 1, 1, 1, 1806390369, 218327374070, 3697211121741701604
Offset: 0
a(5)=1806390369 because this is the smallest number m such that m^2^k + (m+1)^2^k is prime for k=0,1,2,3,4 and 5.
A090875
a(n) is the smallest number m such that m^(2^k) + 2^(2^k) is prime for k=0,1,...,n.
Original entry on oeis.org
1, 1, 1, 1, 1, 2321204055, 37185086099807
Offset: 0
a(5)=2321204055 because 2321204055 is the smallest number m such that m^(2^k) + 2^(2^k) is prime for k=0,1,2,3,4 and 5.
A343120
a(n) is the smallest number b such that (b^(2^k) + 1)/2 is prime for k = 0, 1, ..., n.
Original entry on oeis.org
3, 3, 3, 205, 2326161, 20589460461, 3847314721101
Offset: 0
For n=3, the four numbers (205+1)/2, (205^2+1)/2, (205^4+1)/2, and (205^8+1)/2 are prime, and 205 is smallest with this property, so a(3)=205.
-
a(n)=forstep(b=3,+oo,2,for(k=0,n,!ispseudoprime((b^(2^k)+1)/2)&&next(2));return(b)) \\ if a(n-1) is known, b loop can start from there instead
A343121
a(n) is the least A for which there exists B with 0 < B < A so that A^(2^k) + B^(2^k) is prime for k = 0, 1, ..., n.
Original entry on oeis.org
2, 2, 2, 2, 2, 2669, 34559, 26507494, 3242781025
Offset: 0
For n=5, the six numbers 2669 + 720, 2669^2 + 720^2, 2669^4 + 720^4, 2669^8 + 720^8, 2669^16 + 720^16, and 2669^32 + 720^32 are all prime, and (A,B) = (2669,720) is the least pair with this property, so a(5)=2669.
For n=6, (A,B) = (34559,29000).
For n=7, (A,B) = (26507494,6329559).
For n=8, (A,B) = (3242781025,1554825312).
- Yves Gallot, xgfp8, software for calculating this sequence.
-
a(n)=for(A=1, oo, for(B=1, A-1, for(k=0, n, !ispseudoprime(A^(2^k)+B^(2^k)) && next(2)); return(A)))
Showing 1-10 of 10 results.
Comments