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A251543 a(n) = smallest m such that b(m) is prime and b(m+2)/b(m) = prime(n), where b() = A098550().

%I A251543 #27 Jul 26 2024 05:22:45
%S A251543 2,3,9,101,682,2483,31774,532976
%N A251543 a(n) = smallest m such that b(m) is prime and b(m+2)/b(m) = prime(n), where b() = A098550().
%C A251543 So far a(n) is very roughly 2^(3n-6). Of course it is not known at present if this sequence is infinite (see A098550). It is not even known if there are infinitely many prime terms in A098550. [It is now known that A098550 is a permutation of the natural numbers, so all of the primes appear. See Applegate et al. - _L. Edson Jeffery_, Dec 30 2014]
%C A251543 a(8) appears to deviate from the formula 2^(3n-6) and is closer to 2^19 (than 2^18). - _Chai Wah Wu_, Dec 16 2014
%H A251543 David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, <a href="http://arxiv.org/abs/1501.01669">The Yellowstone Permutation</a>, arXiv preprint arXiv:1501.01669 [math.NT], 2015 and <a href="https://cs.uwaterloo.ca/journals/JIS/VOL18/Sloane/sloane9.html">J. Int. Seq. 18 (2015) 15.6.7</a>.
%t A251543 f[lst_] := Block[{k = 4}, While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k] > 1 || MemberQ[lst, k], k++]; Append[lst, k]]; A098550 = Nest[f, {1, 2, 3}, max = 3000]; b[n_] := A098550[[n]];
%t A251543 a[n_] := For[m = 1, m <= max, m++, If[PrimeQ[b[m]] && b[m+2]/b[m] == Prime[n], Return[m]]];
%t A251543 Do[Print[n, " ", a[n]], {n, 1, 6}] (* _Jean-François Alcover_, Dec 15 2018, after _Robert G. Wilson v_ in A098550 *)
%Y A251543 Cf. A098550, A251542.
%K A251543 nonn,more
%O A251543 1,1
%A A251543 _David Applegate_ and _N. J. A. Sloane_, Dec 15 2014
%E A251543 a(8) from _Chai Wah Wu_, Dec 16 2014