A084199 Smallest prime q < prime(n) such that q+1 divides prime(n)+1, a(n) = 1 if no such q exists.

1, 1, 2, 3, 2, 1, 2, 3, 2, 2, 3, 1, 2, 3, 2, 2, 2, 1, 3, 2, 1, 3, 2, 2, 13, 2, 3, 2, 1, 2, 3, 2, 2, 3, 2, 3, 1, 3, 2, 2, 2, 13, 2, 1, 2, 3, 3, 3, 2, 1, 2, 2, 1, 2, 2, 2, 2, 3, 1, 2, 3, 2, 3, 2, 1, 2, 3, 1, 2, 13, 2, 2, 3, 1, 3, 2, 2, 1, 2, 1, 2, 1, 2, 13, 3, 2, 2, 1, 2, 3, 2, 2, 3, 2, 3, 2, 2, 2, 3, 1, 3, 2, 2

Offset: 1

Author

Reinhard Zumkeller, May 18 2003

Keywords

• nonn

Comments

Conjecture: A008578 is the range of values (or A000040 = range of values > 1).

Links

• Amiram Eldar, Table of n, a(n) for n = 1..10000

Crossrefs

Cf. A000040, A008578, A084196.

Programs

Mathematica

seq[lim_] := Module[{p = Prime[Range[lim]], q, s = {}}, Do[q = SelectFirst[p, Divisible[p[[i]] + 1, # + 1] &]; AppendTo[s, If[q < p[[i]], q, 1]], {i, 1, Length[p]}]; s]; seq[100] (* Amiram Eldar, Mar 28 2025 *)

Formula

a(n) = 1 iff A084196(n) = 0.