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Search: id:A071184
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| A071184 |
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a(1)=1, a(n) is the smallest integer > a(n-1) such that the sum of elements of the simple continued fraction for S(n)=1/a(1)+1/a(2)+...+1/a(n) equals n*(n+1)/2 the n-th triangular number. |
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+0
1
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| 1, 2, 8, 10, 60, 75, 131, 195, 988, 1120, 1130, 1232, 1345, 1347, 1953, 2933, 3549, 9956, 13797, 13970, 14586, 14652, 14903, 17166, 19176, 19634, 22584, 24354, 24842, 26488, 29388, 30840, 31409, 34934, 36059, 45149, 49793, 52690, 59413, 61063
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OFFSET
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1,2
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EXAMPLE
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1/a(1)+1/a(2)+1/a(3)+1/a(4) = (1+1/2+1/8+1/10) which continued fraction is {1, 1, 2, 1, 1, 1, 3} and 1+1+2+1+1+1+3 = 10 = 4*5/2 the fourth triangular number
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PROGRAM
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(PARI) s=1; t=1; for(n=2, 22, s=s+1/t; while(abs(n*(n+1)/2+1-sum(i=1, length(contfrac(s+1/t)), component(contfrac(s+1/t), i)))>0, t++); print1(t, ", "))
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CROSSREFS
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Sequence in context: A062880 A066707 A107227 this_sequence A081231 A121715 A121714
Adjacent sequences: A071181 A071182 A071183 this_sequence A071185 A071186 A071187
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KEYWORD
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easy,nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 10 2002
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EXTENSIONS
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More terms from Lambert Klasen (lambert.klasen(AT)gmx.de), Dec 18 2004
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