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

1, 2211, 333336, 4444671, 5555581345, 666666622350, 777777723060715, 88888888106421690, 9999999993293677081, 101010101010101010104859338144028152581, 1111111111111111111111683873730855571564421

Offset

1,2

Comments

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?

Links

Table of n, a(n) for n=1..11.

Example

a(4) = 4444671 begins with 4444.

Prog

(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)

Crossrefs

Cf. A077692.

Sequence in context: A349098 A238456 A031725 * A253735 A259892 A337160

Adjacent sequences: A077690 A077691 A077692 * A077694 A077695 A077696

Keyword

base,nonn

Author

Amarnath Murthy, Nov 18 2002

Extensions

Corrected and extended by Max Alekseyev, Feb 15 2005

Status

approved