This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.
17 is a term because it factors as 3 x 3 x 3 x 3 in GF(2)[X], and these can be grouped as (3x3x3x3), (3x3 * 3x3), (3 * 3 * 3x3) and (3 * 3 * 3 * 3) that is, as 17, (5 * 5), (3 * 3 * 5) and (3 * 3 * 3 * 3) which give the four different k, 17, 25, 45 and 81, for which A234741(k) = 17. (Note that A236833(17) = 4. In the grouping (3 * 3x3x3) = (3 * 15) 15 is not a prime, so it is discarded,) 25 is not a term because it is an irreducible in GF(2)[X], but not a prime in N. 43 = 3 x 25 is a term because 43 itself is a prime in N. 125 = 3 x 3 x 25 is a term, because both 3 and (3 x 25) = 43 are primes in N. Their product 3*43 = 129 gives one such k that A234741(k) = 125. 1951 = 25 x 87 is a member, as although both 25 and 87 are in A091214, 1951 is itself a prime in N.
25, in binary '11001', encodes polynomial x^4 + x^3 + 1, which is irreducible in polynomial ring GF(2)[X], but is composite in N, thus it is a term of this sequence. 43, in binary '101011', encodes polynomial x^5 + x^3 + x + 1, which factors as (x + 1)(x^4 + x^3 + 1), i.e., 43 = A048720(3,25), and the latter factor of these, encoded by 25, is a composite in N, thus 43 is a term of this sequence.
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