A068499 Numbers m such that m! reduced modulo (m+1) is not zero.

1, 2, 3, 4, 6, 10, 12, 16, 18, 22, 28, 30, 36, 40, 42, 46, 52, 58, 60, 66, 70, 72, 78, 82, 88, 96, 100, 102, 106, 108, 112, 126, 130, 136, 138, 148, 150, 156, 162, 166, 172, 178, 180, 190, 192, 196, 198, 210, 222, 226, 228, 232, 238, 240, 250, 256, 262, 268, 270

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.

Index entries for sequences generated by sieves

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

a(n) = Integer part of A078456(n+1)/A078456(n). - Eric Desbiaux, May 07 2013

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

Crossrefs

Cf. A000040, A039915, A062569, A166460 (almost complement).

Sequence in context: A098392 A076850 A068482 * A137172 A069744 A229362

Adjacent sequences: A068496 A068497 A068498 * A068500 A068501 A068502

Keyword

easy,nonn

Author

Benoit Cloitre, Mar 11 2002

Status

approved