A282344 -id:A282344 - cp's OEIS frontend

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

Ray Chandler, Jul 27 2003

nonn

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

Robert Israel, Table of n, a(n) for n = 1..10000

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

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

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

A282345 Square root of the smallest square referenced in A086982 (Numbers n such that 10^n+1 is not squarefree).

Original entry on oeis.org

11, 7, 11, 13, 11, 7, 11, 11, 7, 13, 11, 17, 11, 7, 11, 19, 11, 7, 13, 101, 11, 7, 487, 11, 7, 11, 73, 11, 7, 11, 11, 13, 7, 11, 11, 7, 29, 11, 17, 11, 7, 11, 11, 7, 11, 13, 19, 11, 7, 11, 137, 11, 7

Offset: 1

Robert Price, Feb 12 2017

nonn

Cf. A086982, A282344.

a(n) = sqrt(A282344(n)). - R. J. Mathar, Feb 13 2017

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

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A282345 Square root of the smallest square referenced in A086982 (Numbers n such that 10^n+1 is not squarefree).

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