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%I #8 Dec 05 2013 19:55:54
%S 1,120,123256,1234806,123457041,12345625545,12345671807241,
%T 123456781852386,123456789378124021,12345678910482682485,
%U 123456789101100044904153,1234567891011124675039766878
%N Smallest triangular number which begins with the concatenation of first n natural numbers.
%e a(4) = 12342996, begins with 1234.
%t t=x={1}; i=4; Do[x=Append[x,n]; While[Take[IntegerDigits[y=i*(i+1)/2],Length[x]]!=x,i++]; AppendTo[t,y],{n,2,7}]; t (* _Jayanta Basu_, May 22 2013 *)
%o (PARI) {rT(m) = ceil((sqrt(8*m+1)-1)/2)} {len10(m) = ceil(log(m+1)/log(10))} {T(n) = (n*(n+1))/2} m=0;for(n=1,20,m=m*10^len10(n)+n;for(k=0,10^6,t=rT(m*10^k);if(T(t)<(m+1)*10^k,print1(" ",T(t));break))) (Alekseyev)
%K base,nonn
%O 1,2
%A _Amarnath Murthy_, Nov 18 2002
%E Corrected and extended by _Max Alekseyev_, Feb 15 2005
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