cp's OEIS Frontend

A372454 a(n) = A372444(n) - A086893(1+A372449(n)).

%I A372454 #9 May 05 2024 21:37:45
%S A372454 6,-48,2560,-1572864,-3848290697216,6649092007880460460883968,
%T A372454 -18999521285301737936647902825311679255527123058688,
%U A372454 76895533293152762966220781422103876125697362804839499718093497881599910128103059800826635129716736
%N A372454 a(n) = A372444(n) - A086893(1+A372449(n)).
%C A372454 The difference between A372444(n) and the term of A086893 with the same binary length.
%H A372454 Antti Karttunen, <a href="/A372454/b372454.txt">Table of n, a(n) for n = 0..10</a>
%F A372454 a(n) = A372444(n) - A086893(1+A000523(A372444(n))).
%F A372454 a(0) = A372453(0) = 6; and for n > 0, a(n) = 4^A372448(n-1) * A372453(n).
%e A372454 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 A372454 The term of A086893 that has same binary length as A372444(1) = 165 is 213, therefore a(1) = 165-213 = -48.
%o A372454 (PARI)
%o A372454 A000523(n) = logint(n,2);
%o A372454 A371094(n) = { my(m=1+3*n, e=valuation(m,2)); ((m*(2^e)) + (((4^e)-1)/3)); };
%o A372454 A372444(n) = { my(x=27); while(n, x=A371094(x); n--); (x); };
%o A372454 A086893(n) = (if(n%2, 2^(n+1), 2^(n+1)+2^(n-1))\3);
%o A372454 A372454(n) = { my(x=A372444(n)); (x - A086893(1+A000523(x))); };
%o A372454 (PARI) A372454(n) = if(!n, A372453(n), (4^A372448(n-1))*A372453(n));
%Y A372454 Cf. A000523, A086893, A372444, A372448, A372449, A372453.
%K A372454 sign
%O A372454 0,1
%A A372454 _Antti Karttunen_, May 05 2024