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.
A085427 =3,2,1,1,2,1,2,1,5,7,5,3,2,1,5,4,2,1,2,1,14,7,26,13,39,22 A(2)=1,A(1)=2 so A(2)=A(1)/2 so M(1)=1 A(5)=1,A(4)=2 but A(5)=A(2) .......... A(21)=7,A(20)=14 A(21)=A(20)/2 and A(21)>A(2) so M(2)=21
A085427 =3,2,1,1,2,1,2,1,5,7,5,3,2,1,5,4,2,1,2,1,14,7,26,13,39,22 A(2)=1,A(1)=2 so A(2)=A(1)/2 so K(1)=1 A(5)=1,A(4)=2 but A(5)=A(2) .......... A(21)=7,A(20)=14 A(21)=A(20)/2 and A(21)>A(2) so K(2)=7
a(3)=2 because 1*2^3 + 1 = 9 is composite, 2*2^3 + 1 = 17 is prime. a(99)=219 because 2^99k + 1 is not prime for k=1,2,...,218. The first term which is not a composite number of this arithmetic progression is 2^99*219 + 1.
sol:=[];m:=1; for n in [0..82] do k:=0; while not IsPrime(k*2^n+1) do k:=k+1; end while; sol[m]:=k; m:=m+1; end for; sol; // Marius A. Burtea, Jun 05 2019
a = {}; Do[k = 0; While[ ! PrimeQ[k 2^n + 1], k++ ]; AppendTo[a, k], {n, 0, 100}]; a (* Artur Jasinski *)
Table[Module[{k=1,n2=2^n},While[!PrimeQ[k*n2+1],k++];k],{n,0,90}] (* Harvey P. Dale, May 25 2024 *)
a(n) = {my(k = 1); while (! isprime(2^n*k+1), k++); k;}
For n = 10, the first primes in the 1024k + 1 arithmetic progression occur at k = 12, 13, 15, 18, 19, ...; 13 is the first odd number, so a(10)=13, while A035050(10)=12. The corresponding primes are 12289 and 13313. For n = 79, the first primes in the (2^79)k + 1 = 604462909807314587353088k + 1 progression occur at k = 36, 44, 104, 249, 296, 299, so a(79)=249, the first odd number, while A035050(79)=36. The two primes arising are 21760664753063325144711169 and 150511264542021332250918913, respectively.
Table[k = 1; While[! PrimeQ[k 2^n + 1], k += 2]; k, {n, 0, 80}] (* Michael De Vlieger, Jul 04 2016 *)
a(n) = k=1; while(!isprime(k*2^n+1), k+=2); k; \\ Michel Marcus, Dec 10 2013
A127587 := proc(n) local k; k:=0 ; while true do if isprime( (k+1)*2^n-1) then RETURN(k) ; fi ; k := k+1 ; od ; end: for n from 0 to 100 do printf("%d, ",A127587(n)) ; od ; # R. J. Mathar, Jan 22 2007
a = {}; Do[k = 0; While[ ! PrimeQ[k 2^n + 2^n - 1], k++ ]; AppendTo[a, k], {n, 0, 50}]; a
a(10)=5 because 5*2^10-1 is prime but 1*2^10-1 and 3*2^10-1 are not.
f[n_] := Block[{k = 1}, While[ !PrimeQ[k*2^n - 1], k += 2]; k]; Table[f@n, {n, 0, 80}] (* Robert G. Wilson v, Feb 20 2007 *)
a(n) = {my(k=1); while(!isprime(k*2^n - 1), k+=2); k}; \\ Indranil Ghosh, Apr 03 2017
from sympy import isprime
def a(n):
k=1
while True:
if isprime(k*2**n - 1): return k
k+=2
print([a(n) for n in range(101)]) # Indranil Ghosh, Apr 03 2017
Table[p=3; prod=6; While[! PrimeQ[prod*2^n-1], p=NextPrime[p]; prod=prod*p]; p, {n, 0, 100}]
primorial = lambda n: prod(primes(n+1)) # includes n, if prime A176994 = lambda n: next(p for p in Primes() if p > 2 and is_pseudoprime(primorial(p)*2**n-1)) # D. S. McNeil, Dec 09 2010
3*2^0-1=2 prime so a(0)=3. 3*2^1-1=5 prime so a(1)=3. 3*2^2-1=11 prime so a(2)=3. 3*2^3-1=23 prime so a(3)=3.
Table[k = 3; While[! PrimeQ[k 2^n - 1], k += 6]; k, {n, 0, 68}] (* Michael De Vlieger, Nov 03 2015 *)
a(n) = {k = 3; while (!isprime(k*2^n-1), k += 6); k;} \\ Michel Marcus, Nov 03 2015
The first few rows are n=2: 1 n=3: 2, 0 n=4: 1, 0 n=5: 2, 0, 0, 3 n=6: 1, 0
T:= proc(n,k) local x;
if igcd(n,k) <> 1 then return NULL fi;
for x from 0 do if isprime(x*n+k) then return x fi
od
end proc:
seq(seq(T(n,k),k=1..n-1),n=2..30);
Table[Map[Catch@ Do[x = 0; While[! PrimeQ[x n + #], x++]; Throw@ x, {10^3}] &, Range@ n /. k_ /; GCD[k, n] > 1 -> Nothing], {n, 2, 19}] // Flatten (* Michael De Vlieger, Jan 06 2016 *)
a[n_] := Module[{k = 1}, While[! PrimeQ @ Floor[2^n/k], k++]; k]; Array[a, 100] (* Amiram Eldar, Aug 31 2020 *)
a(n)=if(n<0,0,k=1; while(isprime(floor(2^n/k)) == 0,k++); k)
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