cp's OEIS Frontend

A335879 a(n) = A332215(A335882(n)).

%I A335879 #21 Jul 10 2020 22:07:07
%S A335879 15,5,30,63,255,10,60,13,126,2047,510,20,120,26,252,4094,262143,11,
%T A335879 1020,4194303,40,240,52,504,8188,61,524286,22,2040,8388606,80,480,104,
%U A335879 1008,16376,122,1048572,140737488355327,44,4080,59,4503599627370495,16777212,160,960,208,2016,32752,244,2097144,253,281474976710654,2417851639229258349412351
%N A335879 a(n) = A332215(A335882(n)).
%C A335879 For all n, a(n) <> A335882(n). Proof: We need to consider only the odd terms, because for n > 1, A332215(2^k * n) = 2^k * A332215(n). The odd terms of A335882 are either primes or semiprimes whose both factors are Mersenne primes, terms of A144482.
%C A335879   (A) If A335882(n) is a prime, then a(n) = A332215(A335882(n)) is a term of A000225 (of the form 2^k - 1, a binary repunit), while primes in A335882 are certainly not of that form, as all Mersenne primes (A000668) are on a different row in array A335430 (on row 1, A335431).
%C A335879   (B) For any semiprime k in A335882, there is only one non-leading zero in the binary representation of A332215(k). On the other hand, a product of two Mersenne primes always contains more than one non-leading zero in its base-2 representation: for three times a Mersenne prime, there are two such zeros, as explained in A279389, and products of two Mersenne primes > 3 are always of the form 8k+1, with at least two zeros immediately left of the least significant 1-bit.
%F A335879 a(n) = A332215(A335882(n)).
%F A335879 For all n >= 1, A007814(a(n)) = A007814(A335882(n)).
%Y A335879 Cf. A000225, A000668, A007814, A279389, A331410, A332215, A335430, A335431, A335882.
%K A335879 nonn
%O A335879 1,1
%A A335879 _Antti Karttunen_, Jul 10 2020