login
Sum of the cubes of the digits of the previous term, starting with 2.
0

%I #25 Oct 20 2024 16:33:23

%S 2,8,512,134,92,737,713,371,371,371,371,371,371,371,371,371,371,371,

%T 371,371,371,371,371,371,371,371,371,371,371,371,371,371,371,371,371,

%U 371,371,371,371,371,371,371,371,371,371,371,371,371,371,371,371,371,371

%N Sum of the cubes of the digits of the previous term, starting with 2.

%C A student of mine (Dennis Vadner) noted this sequence when working with the sequence formed by summing the squares of the digits of the previous term for a class assignment. Upon investigating various initial terms, it was noted that there appeared to be a limited number of end behaviors.

%H Erich Friedman, <a href="https://erich-friedman.github.io/numbers.html">What's Special About This Number?</a>, 371.

%H <a href="/index/Rec#order_01">Index entries for linear recurrences with constant coefficients</a>, signature (1).

%F G.f.: x*(342*x^7 + 24*x^6 - 645*x^5 + 42*x^4 + 378*x^3 - 504*x^2 - 6*x - 2) / (x - 1). - _Jinyuan Wang_, Mar 18 2020

%e Since a(5) = 92, a(6) is therefore 9^3 + 2^3 = 729 + 8 = 737.

%t FixedPointList[Plus@@(IntegerDigits[#]^3) &, 2] (* _Alonso del Arte_, Mar 18 2020 *)

%t PadRight[{2,8,512,134,92,737,713},100,{371}] (* _Harvey P. Dale_, Oct 20 2024 *)

%Y Cf. A000216.

%K nonn,base

%O 1,1

%A Gary Nagel (gary.nagel(AT)sendit.nodak.edu), Oct 12 2004

%E Offset changed to 1 by and more terms from _Jinyuan Wang_, Mar 18 2020