[go: up one dir, main page]

login
A251417
Lengths of runs of identical terms in A251416.
12
1, 1, 1, 5, 1, 5, 1, 6, 1, 7, 1, 12, 8, 10, 1, 17, 8, 1, 13, 13, 13, 5, 10, 11, 5, 9, 8, 19, 10, 11, 7, 11, 5, 9, 27, 9, 13, 5, 23, 5, 9, 17, 9, 11, 11, 7, 21, 9, 7, 5, 17, 27, 11, 7, 9, 17, 5, 13, 9, 21, 11, 7, 13, 9, 9
OFFSET
1,4
COMMENTS
It would be nice to have an alternative description of this sequence, one that is not based on A098550.
It appears (conjecture) that a(n)>1 for n>18. - Alexander R. Povolotsky, Dec 07 2014
Conjecture: a(n) = A247253(n-5) for n>12. - Reinhard Zumkeller, Dec 07 2014
The previous conjecture is equivalent to the statement that A251416(n) lists all primes and only primes after a(30)=18. - M. F. Hasler, Dec 08 2014
LINKS
FORMULA
Let f(n)=A098551(A251595(n)). Then one can prove that A251417(n) = f(n) - f(n-1), n>=2. - Vladimir Shevelev, Dec 09 2014
EXAMPLE
See A251595.
MATHEMATICA
termsOfA251416 = 700;
f[lst_List] := Block[{k = 4}, While[GCD[lst[[-2]], k] == 1 || GCD[lst[[-1]], k] > 1 || MemberQ[lst, k], k++]; Append[lst, k]];
A098550 = Nest[f, {1, 2, 3}, termsOfA251416 - 3];
b[1] = 2;
b[n_] := b[n] = For[k = b[n-1], True, k++, If[FreeQ[A098550[[1 ;; n]], k], Return[k]]];
A251416 = Array[b, termsOfA251416];
Length /@ Split[A251416] (* Jean-François Alcover, Aug 01 2018, after Robert G. Wilson v *)
PROG
(Haskell)
import Data.List (group)
a251417 n = a251417_list !! (n-1)
a251417_list = map length $ group a251416_list
-- Reinhard Zumkeller, Dec 05 2014
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Dec 03 2014
STATUS
approved