A351336 Odd pseudoprimes to base 3; composite terms of A271116.

91, 121, 671, 703, 949, 1105, 1541, 1729, 1891, 2465, 2665, 2701, 2821, 3281, 3367, 3751, 4961, 5551, 6601, 7381, 8401, 8911, 10585, 11011, 12403, 14383, 15203, 15457, 15841, 16471, 16531, 18721, 19345, 23521, 24661, 24727, 28009, 29161, 29341, 30857, 31621

Offset: 1

Author

Bill McEachen, Feb 07 2022

Keywords

• nonn

Comments

Only 2760 of the first 10 million terms of A271116 are nonprimes (0.03%). These composite terms are heavily skewed to rightmost digit = 1.

These odd composites all appear in A005935 (A005935 having an additional 27 terms (all parity 0) through the same term = 179146207).

Links

• Bill McEachen, Table of n, a(n) for n = 1..5767

Crossrefs

Intersection of A002808 and A271116; intersection of A005935 and A005408; subsequence of A038509.

Programs

Mathematica

q[n_] := CompositeQ[n] && Divisible[Round[3^n/12], n]; Select[Range[32000], q] (* Amiram Eldar, Feb 09 2022 *)

PARI

is(n) = (n>1) && !isprime(n) && (lift(Mod(3, 4*n)^(n-1))==1); \\ Michel Marcus, Feb 09 2022; after A271116

PARI

list(lim)=my(v=List()); forcomposite(n=91,lim\1, if(bittest(34,n%6) && Mod(3,n)^(n-1)==1, listput(v,n))); Vec(v) \\ Charles R Greathouse IV, Feb 09 2022

Formula

a(n) ~ (a(n-1)+a(n-2))/2 (conjectured). Bill McEachen, Nov 24 2024