A300406
Primes of the form 13*2^n + 1.
Original entry on oeis.org
53, 3329, 13313, 13631489, 3489660929, 62864142619960717084721153, 5100145160001678120616578906356228963083163798627028041729, 6779255729241169695101387251026410519979286814120235842117075415451380965612384558178346467329, 1735489466685739441945955136262761093114697424414780375581971306355553527196770446893656695635969
Offset: 1
Cf.
A019434,
A039687,
A032356,
A050527,
A050528,
A050529,
A173236,
A195745,
A050526,
A300407,
A300408.
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Filtered(List([1..500],n->13*2^n + 1),IsPrime); # Muniru A Asiru, Mar 06 2018
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[a: n in [1..400] | IsPrime(a) where a is 13*2^n + 1]; // Vincenzo Librandi, Mar 06 2018
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a:=(n,k)->`if`(isprime(k*2^n+1), k*2^n+1, NULL):
seq(a(n,13), n=1..316);
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Select[Table[13 2^n + 1, {n, 400}], PrimeQ] (* Vincenzo Librandi, Mar 06 2018 *)
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lista(nn) = {for(k=1, nn, if(ispseudoprime(p=13*2^k+1), print1(p, ", ")));} \\ Altug Alkan, Mar 29 2018
A291049
Primes of the form 2^r * 17^s + 1.
Original entry on oeis.org
2, 3, 5, 17, 137, 257, 65537, 157217, 295937, 557057, 1336337, 96550277, 1212153857, 2281701377, 5473632257, 395469930497, 1401249857537, 2637646790657, 4964982194177, 28572702478337, 1271035441709057, 38280596832649217, 1872540629620228097, 6634884445436379137
Offset: 1
With n = 1, a(1) = 2^0 * 17^0 + 1 = 2.
With n = 5, a(5) = 2^3 * 17^1 + 1 = 137.
list of (r,s): (0,0), (1,0), (2,0), (4,0), (3,1), (8,0), (16,0), (5,3), (10,2), (15,1), (4,4), (2,6).
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K:=26*10^7+1;; # to get all terms <= K.
A:=Filtered(Filtered([1,3..K],i-> i mod 6=5),IsPrime);; I:=[17];;
B:=List(A,i->Elements(Factors(i-1)));;
C:=List([0..Length(I)],j->List(Combinations(I,j),i->Concatenation([2],i)));;
A291049:=Concatenation([2,3],List(Set(Flat(List([1..Length(C)],i->List([1..Length(C[i])],j->Positions(B,C[i][j]))))),i->A[i]));
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N:= 10^20: # to get all terms <= N+1
S:= NULL:
for r from 0 to ilog2(N) do
for s from 0 to floor(log[17](N/2^r)) do
p:= 2^r*17^s +1;
if isprime(p) then
S:= S, p
fi
od od:
sort([S]); # Robert Israel, Sep 26 2017
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With[{nn = 10^19, q = 17}, Select[Sort@ Flatten@ Table[2^i*q^j + 1, {i, 0, Log[2, nn]}, {j, 0, Log[q, nn/2^i]}], PrimeQ]] (* Michael De Vlieger, Sep 18 2017, after Robert G. Wilson v at A005109 *)
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lista(nn) = my(t, v=List([])); for(r=0, logint(nn, 2), t=2^r; for(s=0, logint(nn\t, 17), if(isprime(t+1), listput(v, t+1)); t*=17)); Vec(vecsort(v)) \\ Jinyuan Wang, Jun 26 2022
Showing 1-2 of 2 results.
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