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.
%I A229289 #56 Feb 22 2021 21:37:19
%S A229289 2,3,5,7,11,13,23,29,31,43,47,53,59,61,67,71,79,107,131,139,157,173,
%T A229289 211,263,269,277,283,311,317,331,347,349,367,373,421,431,461,463,547,
%U A229289 557,599,643,659,661,683,691,709,733,743,787,827,853,859,863,911,941
%N A229289 Primes p of the form p = 2^k * m + 1, where (i) m is squarefree and odd, (ii) all primes that divide m are in the sequence, and (iii) k is 0, 1, or 2.
%C A229289 Taking m=1 in the definition we get the primes 2, 3, 5.
%C A229289 If n is in A226960, then n is a product of terms of this sequence.
%C A229289 If k is only allowed to be 0 or 1, we get 2, 3, 7, 43 and no more. - _Jianing Song_, Feb 21 2021
%C A229289 Also prime factors of terms in A341858. It is conjectured that this sequence is infinite. - _Jianing Song_, Feb 22 2021
%H A229289 Ray Chandler, <a href="/A229289/b229289.txt">Table of n, a(n) for n = 1..1000</a>
%t A229289 fa = FactorInteger; free[n_] := n == Product[fa[n][[i, 1]], {i, Length[fa[n]]}] ; Os[b_, 1] = True; Os[b_, b_] = True; Os[b_, n_] := Os[b, n] = PrimeQ[n] && free[(n - 1)/b^IntegerExponent[n - 1, b]] &&IntegerExponent[n - 1, b] < 3 && Union@Table[Os[b, fa[n - 1][[i, 1]]], {i, Length[fa[n - 1]]}] == {True};G[b_] := Select[Prime[Range[1000]], Os[b, #] &];G[2]
%o A229289 (PARI) is(n)=if(!isprime(n),return(0)); if(n<13,return(1)); my(k=valuation(n-1,2), m=n>>k, f); if(k>2,return(0)); f=factor(m); if(lcm(f[,2])>1, return(0)); for(i=1,#f~, if(!is(f[i,1]), return(0))); 1 \\ _Charles R Greathouse IV_, Oct 28 2013
%Y A229289 Cf. A227007, A226960, A007814, A229290, A229291, A289355, A341858.
%Y A229289 For the complement, see A289355.
%Y A229289 Proper subsequence of A066651.
%K A229289 nonn
%O A229289 1,1
%A A229289 _José María Grau Ribas_, Oct 05 2013
%E A229289 Revised definition from _Charles R Greathouse IV_, Nov 13 2013
%E A229289 Terms corrected by _José María Grau Ribas_, Nov 14 2013