OFFSET
1,1
COMMENTS
The corresponding greatest prime divisors (p, q) of k and k+1 are (2, 3), (2, 3), (3, 5), (5, 7), (7, 11), (3, 5), (11, 13), (7, 11), (19, 23), (23, 29), (5, 7), ...
The pairs of consecutive numbers in the sequence are (8, 9), (20, 21), (114, 115), (169, 170), (2664, 2665), (46864, 46865), (914654, 914655), ...
Conjecturally, this subsequence is probably infinite.
LINKS
Paolo P. Lava, Table of n, a(n) for n = 1..10000 (first 1399 terms from Robert Israel)
EXAMPLE
21 is in the sequence because 21=3*7 and 22=2*11 => 11 is the smallest prime that is larger than 7.
MATHEMATICA
lst={}; Do[If[FactorInteger[n+1][[-1, 1]]==NextPrime[FactorInteger[n][[-1, 1]]], AppendTo[lst, n]], {n, 4000}]; lst
(* Second program: *)
With[{s = Partition[Array[FactorInteger[#][[-1, 1]] &, 3500], 2, 1]}, Rest@ Position[s, _?(#2 == NextPrime@ #1 & @@ # &), 1][[All, 1]] ] (* Michael De Vlieger, Mar 10 2018 *)
PROG
(PARI) isok(k) = {my(f = factor(k)); my(g = factor(k+1)); vecmax(g[, 1]) == nextprime(vecmax(f[, 1])+1); } \\ Michel Marcus, Jul 15 2015
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jul 03 2015
STATUS
approved