OFFSET
1,1
COMMENTS
This sequence is the union of the collection of sequences formed from the nonzero terms of A086981 * A005408, the odd numbers. First occurrence of consecutive integers in sequence is 406,407,408.
From Robert Israel, Feb 13 2017: (Start)
Numbers n such that gcd(n, 10^n + 1) > 1 or n = k*m where k is odd and 2*m is the order of 10 modulo a member of A045616. [Corrected by Jianing Song, Nov 01 2024]
If n is in the sequence, then so is k*n for any odd k. (End)
Numbers of the form k*ord(10,p^2)/2, where k is an odd number and p is a prime such that ord(10,p) is even. Here ord(a,m) is the multiplicative order of a modulo m. Note that if p is not in A045616, then ord(10,p^2) = p*ord(10,p). - Jianing Song, Nov 01 2024
LINKS
Robert Israel, Table of n, a(n) for n = 1..10000
MAPLE
filter:= n -> (n mod 243 = 0 and (n/243)::odd) or igcd(n, (10 &^n +1 mod n)) > 1: # Note that this works if n < 28299156
select(filter, [$1..1000]); # Robert Israel, Feb 13 2017
PROG
(PARI) ord = [1, 486, 56598312]; \\ order of 10 modulo A045616
isA086982(n) = if(gcd(n, 10^n+1) > 1, return(1)); for(i=1, 3, if((ord[i] % 2 == 0) && (n % (ord[i]/2) == 0) && (n/(ord[i]/2) % 2 == 1), return(1))); return(0) \\ Jianing Song, Nov 01 2024, after Robert Israel's comment; considering only the three currently-known terms of A045616
CROSSREFS
KEYWORD
nonn,changed
AUTHOR
Ray Chandler, Jul 27 2003
STATUS
approved