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A075467 Trajectory of 270798 under the Reverse and Add! operation carried out in base 4, written in base 10.

%I A075467 #10 Oct 18 2019 21:14:55
%S A075467 270798,1005135,1994670,5058075,20047500,33313725,66545850,112201785,
%T A075467 225464610,368353785,835135950,1587633825,2841028950,5347819200,
%U A075467 5598498225,10862757750,21453946560,22456662705,43576370550
%N A075467 Trajectory of 270798 under the Reverse and Add! operation carried out in base 4, written in base 10.
%C A075467 The base 4 trajectory of 270798 = A075421(370) provably does not contain a palindrome. A proof along the lines of Klaus Brockhaus, On the 'Reverse and Add!' algorithm in base 2, can be based on the formula given below. - The generating function given describes the sequence from a(11) onward; the g.f. for the complete sequence is known but nearly twice as big.
%H A075467 Klaus Brockhaus, <a href="/A058042/a058042.txt">On the 'Reverse and Add!' algorithm in base 2</a>
%H A075467 <a href="/index/Res#RAA">Index entries for sequences related to Reverse and Add!</a>
%F A075467 a(0), ..., a(10) as above; for n > 10 and n = 5 (mod 6): a(n) = 5*4^(2*k+10)+15341035*4^k-15 where k = (n+1)/6; n = 0 (mod 6): a(n) = 10*4^(2*k+10)+9792150*4^k-10 where k = n/6; n = 1 (mod 6): a(n) = 20*4^(2*k+10)-1305620*4^k where k = (n-1)/6; n = 2 (mod 6): a(n) = 20*4^(2*k+10)+14361820*4^k-15 where k = (n-2)/6; n = 3 (mod 6): a(n) = 40*4^(2*k+10)+7833720*4^k-10 where k = (n-3)/6; n = 4 (mod 6): a(n) = 80*4^(2*k+10)-1305620*4^k where k = (n-4)/6. G.f.: -15*(1426085120*x^11+749251744*x^10+419191024*x^9-1430263104*x^8-715827880*x^7-369055228*x^6-352343296*x^5-222825800*x^4-155978060*x^3+356521280*x^2+189401930*x+105842255)/((x-1)*(x^2+x+1)*(2*x^3-1)*(2*x^3+1)*(4*x^3-1))
%e A075467 270798 (decimal) = 1002013032 -> 1002013032 + 2303102001 = 3311121033 = 1005135 (decimal).
%t A075467 NestWhileList[# + IntegerReverse[#, 4] &, 270798,  # !=
%t A075467 IntegerReverse[#, 4] &, 1, 23] (* _Robert Price_, Oct 18 2019 *)
%o A075467 (PARI) {m=270798; stop=20; c=0; while(c<stop,print1(k=m,","); rev=0; while(k>0,d=divrem(k,4); k=d[1]; rev=4*rev+d[2]); c++; m=m+rev)}
%Y A075467 Cf. A075153, A075421, A075466.
%K A075467 base,nonn
%O A075467 0,1
%A A075467 _Klaus Brockhaus_, Sep 18 2002