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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(). 2
2, 3, 9, 101, 682, 2483, 31774, 532976 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

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

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}] (* Jean-Fran├žois Alcover, Dec 15 2018, after Robert G. Wilson v in A098850 *)

CROSSREFS

Cf. A098550, A251542.

Sequence in context: A054544 A269993 A132537 * A248236 A319157 A153702

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

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Last modified February 27 10:15 EST 2020. Contains 332304 sequences. (Running on oeis4.)