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Search: id:A077693
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| A077693 |
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Smallest triangular number which begins with the concatenation of n times digits of n. |
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+0
3
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| 1, 2211, 333336, 4444671, 5555581345, 666666622350, 777777723060715, 88888888106421690, 9999999993293677081, 101010101010101010104859338144028152581, 1111111111111111111111683873730855571564421
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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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?
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EXAMPLE
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a(4) = 4444671 begins with 4444.
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PROGRAM
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(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)
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CROSSREFS
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Cf. A077692.
Sequence in context: A031635 A031545 A031725 this_sequence A138079 A092992 A091189
Adjacent sequences: A077690 A077691 A077692 this_sequence A077694 A077695 A077696
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KEYWORD
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base,nonn
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AUTHOR
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Amarnath Murthy (amarnath_murthy(AT)yahoo.com), Nov 18 2002
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EXTENSIONS
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Corrected and extended by Max Alekseyev (maxal(AT)cs.ucsd.edu), Feb 15 2005
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