OFFSET
1,2
COMMENTS
Subsidiary sequence: First occurrence of a difference n between successive terms. Conjecture : the maximum value of a(k+1) - a(k) = 7 that too occurs only once for k = 2.( i.e. the subsediary sequence has only 7 terms.)
I conjecture that a(n+1)-a(n) is unbounded. The simplest way to get such a gap is to find n divisible by lcm(1,2,...,k) where n+1 has the same prime signature as n. I expect that such numbers exist, although they are likely to be quite large. (Since n-1 lacks small divisors, it is very likely to be in the sequence and so n is also very likely to be in the sequence.) Note that the sequence includes every prime except 3, 5 and 7. - Franklin T. Adams-Watters, Jul 18 2006
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
MATHEMATICA
sig[n_] := Sort@FactorInteger[n][[;; , 2]]; f[1] = 2; f[n_] := Module[{sign = sig[n], k = n + 1}, While[! CoprimeQ[n, k] || sig[k] == sign, k++]; k]; NestList[f, 1, 100] (* Amiram Eldar, Dec 29 2020 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Amarnath Murthy, Nov 02 2002
EXTENSIONS
More terms from Franklin T. Adams-Watters, Jul 18 2006
STATUS
approved