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A254338 Initial digits of A254143 in decimal representation.

%I A254338 #9 May 13 2015 13:33:56
%S A254338 1,4,7,1,2,3,3,4,6,1,1,2,2,2,3,3,3,4,6,1,1,1,1,1,1,2,2,2,2,2,2,3,3,3,
%T A254338 3,4,4,6,1,1,1,1,1,1,1,1,1,1,2,2,2,2,2,2,2,2,2,2,3,3,3,3,3,4,4,6,1,1,
%U A254338 1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,2
%N A254338 Initial digits of A254143 in decimal representation.
%C A254338 a(n) = A000030(A254143(n));
%C A254338 also initial digits of A254323: a(n) = A000030(A254323(n)).
%C A254338 all terms are of the form u*v mod 10, where u <= v and belonging to {1,3,4,6,7}, the distinct elements of A254397:
%C A254338 length of k-th run of consecutive 1s = A005993(k-2), k > 1;
%C A254338 length of k-th run of consecutive 2s = k*(k+1)/2 = A000217(k), k >= 1;
%C A254338 length of k-th run of consecutive 3s = k+1, k >= 1;
%C A254338 length of k-th run of consecutive 4s = A065033(k-1);
%C A254338 n with a(n) = 4: A237424(n) = (10^a+10^b+1)/3 with b = 0, see also A093137, A133384;
%C A254338 n with a(n) = 6: A237424(n) = (10^a+10^b+1)/3 with a = b; A005994(a(n)) = 6 for n > 1; see also A199682;
%H A254338 Reinhard Zumkeller, <a href="/A254338/b254338.txt">Table of n, a(n) for n = 1..10000</a>
%o A254338 (Haskell)
%o A254338 a254338 = a000030 . a254143
%o A254338 (PARI) listA237424(lim)=my(v=List(),a,t); while(1, for(b=0,a, t=(10^a+10^b+1)/3; if(t>lim, return(Set(v))); listput(v, t)); a++)
%o A254338 do(lim)=my(v=List(),u=listA237424(lim),t); for(i=1,#u, for(j=1,i, t=u[i]*u[j]; if(t>lim,break); listput(v,t))); apply(n->digits(n)[1], Set(v)) \\ _Charles R Greathouse IV_, May 13 2015
%Y A254338 Cf. A254143, A254323, A000030, A254339, A005993, A000217, A065033.
%K A254338 nonn,base
%O A254338 1,2
%A A254338 _Reinhard Zumkeller_, Feb 27 2015