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A248078 a(1) = 1; a(n+1) = a(n) + product of digits of a(n) + sum of digits of a(n).

%I A248078 #20 Sep 11 2019 20:26:24
%S A248078 1,3,9,27,50,55,90,99,198,288,434,493,617,673,815,869,1324,1358,1495,
%T A248078 1694,1930,1943,2068,2084,2098,2117,2142,2167,2267,2452,2545,2761,
%U A248078 2861,2974,3500,3508,3524,3658,4400,4408,4424,4566,5307,5322,5394,5955,7104,7116
%N A248078 a(1) = 1; a(n+1) = a(n) + product of digits of a(n) + sum of digits of a(n).
%C A248078 Unlike A063108, this sequence includes in its formula the digit 0 in the product of digits of a(n).
%H A248078 Robert Israel, <a href="/A248078/b248078.txt">Table of n, a(n) for n = 1..10000</a>
%e A248078 Given a(5)=50, then a(6)=50+(5+0)+(5*0)=55.
%p A248078 f:= proc(x) local L;
%p A248078   L:= convert(x,base,10);
%p A248078   x + convert(L,`+`)+convert(L,`*`)
%p A248078 end proc:
%p A248078 A[1]:= 1:
%p A248078 for n from 2 to 100 do A[n]:= f(A[n-1]) od:
%p A248078 seq(A[i],i=1..100); # _Robert Israel_, Jun 25 2019
%t A248078 NestList[#+Total[IntegerDigits[#]]+Times@@IntegerDigits[#]&,1,50] (* _Harvey P. Dale_, Sep 11 2019 *)
%o A248078 (PARI) lista(nn) = {prev = 1; print1(prev, ", "); for (n=1, nn, d = digits(prev); prev += sumdigits(prev) + prod(k=1, #d, d[k]); print1(prev, ", "););} \\ _Michel Marcus_, Oct 01 2014
%Y A248078 Cf. A063108, A004207.
%K A248078 nonn,base,easy,look
%O A248078 1,2
%A A248078 _Gil Broussard_, Sep 30 2014