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%I #34 Sep 08 2022 08:46:25
%S 0,10,1,11,2,12,3,13,4,14,5,15,6,16,7,17,8,18,9,19,25,71,24,23,51,32,
%T 115,117,33,61,171,91,52,711,133,1117,125,42,116,81,313,1171,152,118,
%U 215,124,1711,251,142,7111,512,181,521,214,111117,26,222,123,132,161,241,111171,34,111711,43,117111,62,412
%N The digitsum of a(n) is the product of the digits of a(n+1).
%C This is the lexicographically earliest infinite sequence of distinct nonnegative terms with this property; a(1) and a(2) are the only terms containing a zero.
%H Carole Dubois, <a href="/A332177/b332177.txt">Table of n, a(n) for n = 1..1342</a>
%e a(20) = 19 and a(21) = 25; the digitsum of 19 is 10 and 10 is 2*5;
%e a(21) = 25 and a(22) = 71; the digitsum of 25 is 7 and 7 is 7*1;
%e a(22) = 71 and a(23) = 24; the digitsum of 71 is 8 and 8 is 2*4;
%e a(23) = 24 and a(25) = 23; the digitsum of 24 is 6 and 6 is 2*3; etc.
%o (Magma) a:=[0,10]; for m in [3..70] do k:=1; while k in a or (IsPrime(&+Intseq(k)) and &+Intseq(k) ge 11) or &*Intseq(k) ne &+Intseq(a[m-1]) do k:=k+1; end while; Append(~a,k); end for; a; // _Marius A. Burtea_, Oct 16 2020
%Y Cf. A330521.
%K base,nonn
%O 1,2
%A _Eric Angelini_ and _Carole Dubois_, Oct 02 2020
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