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.
197 = 2^2*7^2 + 1 is a member.
Select[Prime[Range[110]],Length[Select[FactorInteger[#-1] [[All, 1]], OddQ]]<2&] (* Harvey P. Dale, Oct 09 2017 *)
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).
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]));
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
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 *)
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
N:= 1000: # to get all terms <= N
Primes:= select(isprime, [$3..(N+1)/2]):
sort(convert(select(isprime, {2,seq(seq(seq(2^r*p^s-1, r = 1 .. ilog2((N+1)/p^s)),s=0..floor(log[p]((N+1)/2))),p=Primes)}),list)); # Robert Israel, Jun 13 2018
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