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A112543
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Numerators of fractions n/m in array by anti-diagonals.
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1
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1, 2, 1, 3, 1, 1, 4, 3, 2, 1, 5, 2, 1, 1, 1, 6, 5, 4, 3, 2, 1, 7, 3, 5, 1, 3, 1, 1, 8, 7, 2, 5, 4, 1, 2, 1, 9, 4, 7, 3, 1, 2, 3, 1, 1, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 11, 5, 3, 2, 7, 1, 5, 1, 1, 1, 1, 12, 11, 10, 9, 8, 7, 6, 5, 4, 3, 2, 1, 13, 6, 11, 5, 9, 4, 1, 3, 5, 2, 3, 1, 1, 14, 13, 4, 11, 2, 3, 8, 7, 2
(list; table; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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LINKS
| Eric Weisstein's World of Mathematics, Exponential Integral
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FORMULA
| For n/m: g.f.: x/(1-x)*log(1/(1-y)), e.g.f.: x*e^x*(Ei(y)-log(y)+gamma) = x*e^x*integral_t=0^y (e^t-1)dt.
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EXAMPLE
| a(2,4)=1/2 because 2/4 = 1/2.
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PROG
| (PARI) t1(n)=binomial(floor(3/2+sqrt(2*n)), 2)-n+1 t2(n)=n-binomial(floor(1/2+sqrt(2*n)), 2) vector(100, n, t1(n)/gcd(t1(n), t2(n)))
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CROSSREFS
| Denominators in A112544. Reduced version of A004736/A002260.
Sequence in context: A011973 A115139 A198788 * A099478 A133913 A141412
Adjacent sequences: A112540 A112541 A112542 * A112544 A112545 A112546
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KEYWORD
| easy,frac,nonn,tabl
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AUTHOR
| Frank Adams-Watters (FrankTAW(AT)Netscape.net), Sep 11 2005
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EXTENSIONS
| Keyword tabl added by Franklin T. Adams-Watters (FrankTAW(AT)Netscape.net), Sep 02 2009
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