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A259672
Number k such that the greatest prime divisor of k+1 is the smallest prime that is larger than the greatest prime divisor of k.
1
2, 8, 9, 20, 21, 24, 77, 98, 114, 115, 125, 169, 170, 175, 363, 423, 464, 516, 530, 782, 832, 902, 961, 1147, 1206, 1245, 1274, 1449, 1659, 1829, 1862, 2079, 2085, 2108, 2299, 2400, 2431, 2600, 2627, 2664, 2665, 2736, 2781, 2783, 2914, 3013, 3024, 3255, 3416
OFFSET
1,1
COMMENTS
Numbers k such that A006530(k+1) = A151800(A006530(k)).
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
Sequence in context: A096033 A073413 A046681 * A163619 A166968 A075644
KEYWORD
nonn
AUTHOR
Michel Lagneau, Jul 03 2015
STATUS
approved