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A077693 Smallest triangular number which begins with the concatenation of n times digits of n. 2

%I

%S 1,2211,333336,4444671,5555581345,666666622350,777777723060715,

%T 88888888106421690,9999999993293677081,

%U 101010101010101010104859338144028152581,1111111111111111111111683873730855571564421

%N Smallest triangular number which begins with the concatenation of n times digits of n.

%C 21, 2211, 222111, 22221111, ...and 6, 561, 55611, 5556111, 555561111 give patterned triangular number sequences of patterned number sequences 6, 66, 666, ... and 3, 33, 333, ...respectively. Are there any other patterns?

%e a(4) = 4444671 begins with 4444.

%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} for(n=1,20,l=len10(n);m=n*(10^(l*n)-1)/(10^l-1);for(k=0,10^6,t=rT(m*10^k);if(T(t)<(m+1)*10^k,print1(" ",T(t));break))) (Alekseyev)

%Y Cf. A077692.

%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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Last modified January 24 00:05 EST 2022. Contains 350515 sequences. (Running on oeis4.)