%I #17 Jan 06 2022 20:20:07
%S 1,2,4,15,223,49723,2472376715,6112646620874191195,
%T 37364448711684668107465232045415527964,
%U 1396102027528114054292352968370664257124645724783116404170065476248865985173
%N a(0) = 1, a(n+1) = a(n)^2 + 1 - floor(log_2(a(n))).
%C a(0) = 1, a(n+1) = A002522(a(n)) - A000523(a(n)).
%H <a href="/index/Aa#AHSL">Index entries for sequences of form a(n+1)=a(n)^2 + ...</a>
%p a:= proc(n) option remember; `if`(n=0, 1,
%p (t-> t^2 + 1 - ilog2(t))(a(n-1)))
%p end:
%p seq(a(n), n=0..9); # _Alois P. Heinz_, Jan 06 2022
%t NestList[#^2+1-Floor[Log2[#]]&,1,10] (* _Harvey P. Dale_, Jan 06 2022 *)
%o (PARI) first(n) = my(t = 1, res = List([1])); for(i= 1, n-1, t = t^2 + 1 - logint(t, 2); listput(res, t)); res \\ _David A. Corneth_, Jan 06 2022
%Y Cf. A000523, A002522.
%K nonn
%O 0,2
%A _Reinhard Zumkeller_, Nov 25 2004
%E Corrected by _Harvey P. Dale_, Jan 06 2022