%I #9 May 05 2024 21:37:45

%S 6,-48,2560,-1572864,-3848290697216,6649092007880460460883968,

%T -18999521285301737936647902825311679255527123058688,

%U 76895533293152762966220781422103876125697362804839499718093497881599910128103059800826635129716736

%N a(n) = A372444(n) - A086893(1+A372449(n)).

%C The difference between A372444(n) and the term of A086893 with the same binary length.

%H Antti Karttunen, <a href="/A372454/b372454.txt">Table of n, a(n) for n = 0..10</a>

%F a(n) = A372444(n) - A086893(1+A000523(A372444(n))).

%F a(0) = A372453(0) = 6; and for n > 0, a(n) = 4^A372448(n-1) * A372453(n).

%e The term of A086893 that has same binary length as A372444(0) = 27 is 21 [as 21 = 10101_2 in binary, and 27 = 11011_2 in binary], therefore a(0) = 27-21 = 6.

%e The term of A086893 that has same binary length as A372444(1) = 165 is 213, therefore a(1) = 165-213 = -48.

%o (PARI)

%o A000523(n) = logint(n,2);

%o A371094(n) = { my(m=1+3*n, e=valuation(m,2)); ((m*(2^e)) + (((4^e)-1)/3)); };

%o A372444(n) = { my(x=27); while(n, x=A371094(x); n--); (x); };

%o A086893(n) = (if(n%2, 2^(n+1), 2^(n+1)+2^(n-1))\3);

%o A372454(n) = { my(x=A372444(n)); (x - A086893(1+A000523(x))); };

%o (PARI) A372454(n) = if(!n, A372453(n), (4^A372448(n-1))*A372453(n));

%Y Cf. A000523, A086893, A372444, A372448, A372449, A372453.

%K sign,new

%O 0,1

%A _Antti Karttunen_, May 05 2024