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A338845 No nonprime digit is present in a(n) * a(n+1).

%I A338845 #10 Nov 18 2020 20:04:18
%S A338845 1,2,11,3,9,8,4,13,21,12,6,37,15,5,7,36,62,86,27,101,22,16,17,19,28,
%T A338845 84,33,69,83,31,25,23,14,18,29,77,49,48,74,78,94,38,194,378,199,127,
%U A338845 175,43,54,143,39,57,41,55,61,53,44,58,134,248,224,123,45,75,47,59,97,26,202,161,157,46,82,271,87,256
%N A338845 No nonprime digit is present in a(n) * a(n+1).
%C A338845 The nonprime digits are 0, 1, 4, 6, 8 and 9. This is the lexicographically earliest sequence of distinct positive terms with this property.
%H A338845 Robert Israel, <a href="/A338845/b338845.txt">Table of n, a(n) for n = 1..6500</a>
%e A338845 a(1) * a(2) = 1 * 2 = 2 (no nonprime digit is present);
%e A338845 a(2) * a(3) = 2 * 11 = 22 (no nonprime digit is present);
%e A338845 a(3) * a(4) = 11 * 3 = 33 (no nonprime digit is present);
%e A338845 a(4) * a(5) = 3 * 9 = 27 (no nonprime digit is present); etc.
%p A338845 N:= 500: # for terms before the first term >= N
%p A338845 S:= select(t -> t mod 10 <> 0, [$2...N]):
%p A338845 nS:= nops(S):
%p A338845 V:=Vector(N):
%p A338845 V[1]:= 1:
%p A338845 for n from 2 do
%p A338845   for i from 1 to nS+2-n do
%p A338845     s:= S[i];
%p A338845     if convert(convert(V[n-1]*s,base,10),set) subset {2,3,5,7} then
%p A338845       V[n]:= s;
%p A338845       S:= subsop(i=NULL,S);
%p A338845       break
%p A338845     fi;
%p A338845   od;
%p A338845   if V[n] = 0 then break fi;
%p A338845 od:
%p A338845 convert(V[1..n-1],list); # _Robert Israel_, Nov 18 2020
%t A338845 Block[{a = {1}}, Do[Block[{k = 1}, While[Nand[FreeQ[a, k], NoneTrue[IntegerDigits@ Total[a[[-1]]*k], ! PrimeQ@ # &]], k++]; AppendTo[a, k]], {i, 2, 76}]; a] (* _Michael De Vlieger_, Nov 12 2020 *)
%Y A338845 Cf. A338839, A338840, A338841, A338842, A338843, A338844, A338846 (variants on the same idea).
%K A338845 base,nonn
%O A338845 1,2
%A A338845 _Eric Angelini_ and _Carole Dubois_, Nov 11 2020