A344185 -id:A344185 - cp's OEIS frontend

0, 3, 3, 3, 5, 3, 3, 27, 3, 9, 5, 9, 27, 33, 3, 43, 9, 9, 39, 9, 5, 3, 33, 27, 9, 27, 39, 3, 5, 3, 9, 141, 1025, 129, 5, 513, 83, 99, 17, 57, 9, 129, 89, 33, 27, 3, 33, 45, 513, 29, 75, 9, 71, 513, 129, 149, 17, 524289, 149, 3, 39, 536870913, 3, 27, 262145, 9, 39, 513, 101, 43

Offset: 1

Jianing Song, May 11 2021

nonn

A more intuitive version of A344142.
In A057496 it is stated that if x^n + x^3 + x^2 + x + 1 is irreducible, then so is x^n + x^3 + 1. It follows that no term can be equal to 15.
It is conjectured that an irreducible polynomial of degree n with 5 terms exists for every n. It follows from the conjecture that for n >= 2, a(n) is of the form 2^k + 1 or an odd number with Hamming weight 4.
It is conjectured that no term can be of the form P_m(2^k), where P_m(x) = Product_{i>=0} (1 + x^(2^(d_i)))^(c_i) if the binary representation of m is m = Sum_{i>=0} c_i * 2^(d_i), k is an odd number. See my conjecture in A344177.

			See A344142.

Jianing Song, Table of n, a(n) for n = 1..1000

Cf. A014580, A344142, A344185, A344177.

A344186(n) = if(n==1, 0, for(k=1, n-1, if(polisirreducible(Mod(x^n+x^k+1, 2)), return(2^k+1))); for(a=3, n-1, for(b=2, a-1, for(c=1, b-1, if(polisirreducible(Mod(x^n+x^a+x^b+x^c+1, 2)), return(2^a+2^b+2^c+1)))))) \\ Assuming that an irreducible polynomial of degree n with at most 5 terms exists for every n.

cp's OEIS Frontend

A344186 a(n) = A344142(n) - 2^n.

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