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

2, 3, 9, 101, 682, 2483, 31774, 532976

Offset: 1

Author

David Applegate and N. J. A. Sloane, Dec 15 2014

Keywords

• nonn
• more

Comments

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]

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

Links

• David L. Applegate, Hans Havermann, Bob Selcoe, Vladimir Shevelev, N. J. A. Sloane, and Reinhard Zumkeller, The Yellowstone Permutation, arXiv preprint arXiv:1501.01669 [math.NT], 2015 and J. Int. Seq. 18 (2015) 15.6.7.

Crossrefs

Cf. A098550, A251542.

Programs

Mathematica

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]];
a[n_] := For[m = 1, m <= max, m++, If[PrimeQ[b[m]] && b[m+2]/b[m] == Prime[n], Return[m]]];
Do[Print[n, " ", a[n]], {n, 1, 6}] (* Jean-François Alcover, Dec 15 2018, after Robert G. Wilson v in A098550 *)

Extensions

a(8) from Chai Wah Wu, Dec 16 2014