

A251543


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


2




OFFSET

1,1


COMMENTS

So far a(n) is very roughly 2^(3n6). 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^(3n6) and is closer to 2^19 (than 2^18).  Chai Wah Wu, Dec 16 2014


LINKS

Table of n, a(n) for n=1..8.
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.


MATHEMATICA

f[lst_] := Block[{k = 4}, While[GCD[lst[[2]], k] == 1  GCD[lst[[1]], k] > 1  MemberQ[lst, k], k++]; Append[lst, k]]; A098850 = Nest[f, {1, 2, 3}, max = 3000]; b[n_] := A098850[[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}] (* JeanFrançois Alcover, Dec 15 2018, after Robert G. Wilson v in A098850 *)


CROSSREFS

Cf. A098550, A251542.
Sequence in context: A269993 A132537 A333474 * A332203 A248236 A319157
Adjacent sequences: A251540 A251541 A251542 * A251544 A251545 A251546


KEYWORD

nonn,more


AUTHOR

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


EXTENSIONS

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


STATUS

approved



