cp's OEIS Frontend

A349102 Increase the odd part of n to the next greater odd number.

%I A349102 #14 Mar 27 2022 13:38:06
%S A349102 3,6,5,12,7,10,9,24,11,14,13,20,15,18,17,48,19,22,21,28,23,26,25,40,
%T A349102 27,30,29,36,31,34,33,96,35,38,37,44,39,42,41,56,43,46,45,52,47,50,49,
%U A349102 80,51,54,53,60,55,58,57,72,59,62,61,68,63,66,65,192,67,70,69
%N A349102 Increase the odd part of n to the next greater odd number.
%C A349102 This is +2 at the bit position of the odd part of n, that being the least significant 1-bit.
%C A349102 The least significant run of 1-bits changes from 0111..111 in n to 1000..001 in a(n).
%C A349102 Arrays A054582 and A135764 arrange terms into rows having the same number of trailing 0 bits. a(n) is the term to the right of n, i.e., next in its row.
%H A349102 Michael De Vlieger, <a href="/A349102/b349102.txt">Table of n, a(n) for n = 1..10000</a>
%F A349102 a(n) = n + A171977(n).
%F A349102 a(2*n) = 2*a(n).
%F A349102 a(2*n+1) = 2*n + 3.
%e A349102 n    = 3448 = binary 1101 0111 1 000
%e A349102 a(n) = 3464 = binary 1101 1000 1 000
%t A349102 Array[# + 2^(IntegerExponent[#, 2] + 1) &, 67] (* _Michael De Vlieger_, Mar 27 2022 *)
%o A349102 (PARI) a(n) = n + 2<<valuation(n,2);
%Y A349102 Cf. A000265 (odd part), A171977 (2 at odd part), A285326.
%Y A349102 Arrays: A054582, A135764.
%K A349102 nonn,easy
%O A349102 1,1
%A A349102 _Kevin Ryde_, Mar 26 2022