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A036066 The summarize Lucas sequence: summarize the previous two terms, start with 1, 3.

%I A036066 #17 Jun 18 2022 13:32:18
%S A036066 1,3,1311,2331,331241,14432231,34433241,54533231,2544632221,
%T A036066 163534435221,263544436231,363554634231,463554733221,17364544733221,
%U A036066 37263554634231,37363554734231,37364544933221,1937263554933221,3927263544835231,391827264534836231,293827363544836231
%N A036066 The summarize Lucas sequence: summarize the previous two terms, start with 1, 3.
%C A036066 After the 26th term the sequence goes into a cycle of 46 terms.
%C A036066 "Summarize" uses here method C = A244112: in order of decreasing digit value.
%H A036066 Alois P. Heinz, <a href="/A036066/b036066.txt">Table of n, a(n) for n = 0..1000</a>
%H A036066 <a href="/index/Sa#swys">Index to sequences related to say what you see</a>
%F A036066 a(n+1) = A244112(concat(a(n),a(n-1))). - _M. F. Hasler_, Feb 25 2018
%p A036066 a:= proc(n) option remember; `if`(n<2, 2*n+1, (p-> parse(cat(seq((c->
%p A036066      `if`(c=0, [][], [c, 9-i][]))(coeff(p, x, 9-i)), i=0..9))))(
%p A036066       add(x^i, i=map(x-> convert(x, base, 10)[], [a(n-1),a(n-2)]))))
%p A036066     end:
%p A036066 seq(a(n), n=0..20);  # _Alois P. Heinz_, Jun 18 2022
%t A036066 a[0] = 1; a[1] = 3; a[n_] := a[n] = FromDigits @ Flatten @ Reverse @ Select[ Transpose @ { DigitCount[a[n-1]] + DigitCount[a[n-2]], Append[ Range[9], 0]}, #[[1]] > 0 &];
%t A036066 Table[a[n], {n, 0, 17}] (* _Jean-François Alcover_, Dec 30 2017 *)
%o A036066 (PARI) {a=[1,3]; for(n=1,50,a=concat(a,A244112(eval(Str(a[n],a[n+1]))))); a} \\ _M. F. Hasler_, Feb 25 2018
%Y A036066 Cf. A036059.
%Y A036066 Cf. A244112 (summarizing as used here: by decreasing digit value), A047842 (alternative summarizing method: by increasing digit value), A047843 (another method: don't omit missing digits between smallest and largest one).
%K A036066 base,easy,nice,nonn
%O A036066 0,2
%A A036066 _Floor van Lamoen_