A086982 Numbers n such that 10^n+1 is not squarefree.

11, 21, 33, 39, 55, 63, 77, 99, 105, 117, 121, 136, 143, 147, 165, 171, 187, 189, 195, 202, 209, 231, 243, 253, 273, 275, 292, 297, 315, 319, 341, 351, 357, 363, 385, 399, 406, 407, 408, 429, 441, 451, 473, 483, 495, 507, 513, 517, 525, 539, 548, 561, 567

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

Cf. A005408, A013929, A086981, A045616, A049096, A282344, A282345.

Sequence in context: A264646 A139113 A109335 * A145060 A146246 A215968

Adjacent sequences: A086979 A086980 A086981 * A086983 A086984 A086985

Keyword

nonn

Author

Ray Chandler, Jul 27 2003

Status

approved