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A121167 a(1)=1; a(n) = the reversal of (a(n-1) + spd(a(n-1))), where spd(n) is the sum of d^d for d the digits of n (with 0^0 = 1).

%I A121167 #18 Oct 15 2024 00:02:50
%S A121167 1,2,6,26664,298661,386985404,646010808,218856976,288157046,460585223,
%T A121167 736514774,427530937,259106618,767004366,507197867,489519319,
%U A121167 2141658661,3329758512,3706874373,2129616273,8563597152,3644768698,9667076604
%N A121167 a(1)=1; a(n) = the reversal of (a(n-1) + spd(a(n-1))), where spd(n) is the sum of d^d for d the digits of n (with 0^0 = 1).
%C A121167 Eventually periodic with period 7978, as a(23895) = a(31873) = 3365361711. - _Robert Israel_, Oct 13 2024
%H A121167 Robert Israel, <a href="/A121167/b121167.txt">Table of n, a(n) for n = 1..37363</a>
%p A121167 f(0):= 1: for i from 1 to 9 do f(i):= i^i od:
%p A121167 rev:= proc(n) local L,i;
%p A121167   L:= convert(n,base,10);
%p A121167   add(L[-i]*10^(i-1),i=1..nops(L))
%p A121167 end proc:
%p A121167 R:= 1: x:= 1:
%p A121167 for n from 1 to 25 do
%p A121167   x:= rev(x + convert(map(f, convert(x,base,10)),`+`));
%p A121167   R:= R,x
%p A121167 od:
%p A121167 R; # _Robert Israel_, Oct 13 2024
%t A121167 s={1};fn[n_]:=If[n>0,n^n,1]; Do[AppendTo[s,IntegerReverse[Total[fn/@IntegerDigits[s[[-1]]]]+s[[-1]]]],{n,22}];s (* _James C. McMahon_, Oct 13 2024 *)
%Y A121167 Cf. A045503 (spd).
%K A121167 base,easy,nonn,look
%O A121167 1,2
%A A121167 _Jason Earls_, Aug 14 2006
%E A121167 Name clarified by _Robert Israel_, Oct 13 2024