cp's OEIS Frontend

A331469 a(n) is the greatest value of the form p_1 + ... + p_k where p_1, ..., p_k are powers of primes and such that the concatenation of the binary representations of p_1, ..., p_k equals the binary representation of n.

%I A331469 #11 Jan 19 2020 06:28:02
%S A331469 1,2,3,4,5,3,7,8,9,4,11,5,13,5,8,16,17,6,19,6,7,7,23,9,25,5,27,7,29,9,
%T A331469 31,32,17,10,18,8,37,11,20,10,41,6,43,9,15,13,47,17,49,7,26,7,53,15,
%U A331469 28,11,26,7,59,11,61,10,32,64,33,18,67,12,13,19,71,12
%N A331469 a(n) is the greatest value of the form p_1 + ... + p_k where p_1, ..., p_k are powers of primes and such that the concatenation of the binary representations of p_1, ..., p_k equals the binary representation of n.
%C A331469 We can always split the binary representation of a number into powers of 2, so the sequence is well defined.
%H A331469 Rémy Sigrist, <a href="/A331469/b331469.txt">Table of n, a(n) for n = 1..8192</a>
%H A331469 Rémy Sigrist, <a href="/A331469/a331469.gp.txt">PARI program for A331469</a>
%H A331469 <a href="/index/Bi#binary">Index entries for sequences related to binary expansion of n</a>
%F A331469 a(n) >= A162439(n).
%F A331469 a(n) <= n with equality iff n is a power of a prime.
%e A331469 For n = 22:
%e A331469 - the binary representation of 22 is "10110",
%e A331469 - we can split it into "10" and "1" and "10" (2^1 and 2^0 and 2^1),
%e A331469 - or into "101" and "10" (5^2 and 2^1),
%e A331469 - hence a(22) = max(5, 7) = 7.
%o A331469 (PARI) See Links section.
%Y A331469 Cf. A000961, A162439, A331362.
%K A331469 nonn,base
%O A331469 1,2
%A A331469 _Rémy Sigrist_, Jan 17 2020