OFFSET
1,2
COMMENTS
Also n such that tau((n+1)!) = 2* tau(n!)
For n > 2, a(n) is the smallest number such that a(n) !== -1 (mod a(k)+1) for any 1 < k < n. [Franklin T. Adams-Watters, Aug 07 2009]
Also n such that sigma((n+1)!) = (n+2)* sigma(n!), which is the same as A062569(n+1) = (n+2)*A062569(n). - Zak Seidov, Aug 22 2012
This sequence is obtained by the following sieve: keep 1 in the sequence and then, at the k-th step, keep the smallest number, x say, that has not been crossed off before and cross off all the numbers of the form k*(x + 1) - 1 with k > 1. The numbers that are left form the sequence. - Jean-Christophe Hervé, Dec 12 2015
a(n) = A039915(n-1) for 3 < n <= 1000. - Georg Fischer, Oct 19 2018
LINKS
Jean-Christophe Hervé, Table of n, a(n) for n = 1..10000
David J. Hemmer and Karlee J. Westrem, Palindrome Partitions and the Calkin-Wilf Tree, arXiv:2402.02250 [math.CO], 2024. See Remark 3.3 p. 6.
FORMULA
For n >= 4, a(n) = prime(n-1) - 1 = A006093(n-1).
For n <> 3, all terms are one less prime. - Zak Seidov, Aug 22 2012
EXAMPLE
Illustration of the sieve: keep 1 = a(1) and then
1st step: take 2 = a(2) and cross off 5, 8, 11, 14, 17, 20, 23, 26, etc.
2nd step: take 3 = a(3) and cross off 7, 11, 15, 19, 23, 27, etc.
3rd step: take 4 = a(4) and cross off 9, 14, 19, 24, etc.
4th step: take 6 = a(5) and cross off 13, 19, 25 etc.
10 is obtained at next step and the smallest crossed off numbers are then 21 and 28. This gives the beginning of the sequence up to 22 = a(10): 1, 2, 3, 4, 6, 10, 12, 16, 18, 22. - Jean-Christophe Hervé, Dec 12 2015
MATHEMATICA
Select[Range[300], Mod[#!, #+1]!=0&] (* Harvey P. Dale, Apr 11 2012 *)
PROG
(PARI) {plnt=1 ; nfa=1; mxind=60 ; for(k=1, 10^7, nfa=nfa*k;
if(nfa % (k+1) != 0 , print1(k, ", "); plnt++ ;
if(mxind < plnt, break() )))} \\ Douglas Latimer, Apr 25 2012
(PARI) a(n)=if(n<5, n, prime(n-1)-1) \\ Charles R Greathouse IV, Apr 25 2012
(Python)
from sympy import prime
def A068499(n): return prime(n-1)-1 if n>3 else n # Chai Wah Wu, Aug 27 2024
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Benoit Cloitre, Mar 11 2002
STATUS
approved