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A056053 a(n) = smallest odd number 2m+1 such that the partial sum of the odd harmonic series Sum_{j=0..m} 1/(2j+1) is > n. 9
3, 15, 113, 837, 6183, 45691, 337607, 2494595, 18432707, 136200301, 1006391657, 7436284415, 54947122715, 406007372211, 3000011249847, 22167251422541, 163795064320251, 1210290918990281, 8942907496445513, 66079645178783351 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

REFERENCES

Calvin C. Clawson, "Mathematical Mysteries, The Beauty and Magic of Numbers," Plenum Press, NY and London, 1996, page 64.

LINKS

Table of n, a(n) for n=1..20.

FORMULA

a(n) ~= floor( (1/2)*A002387(2n)).

The next term is approximately the previous term * e^2.

a(n) = A092315(n)*2 + 1 = floor(exp(n*2-Euler)/4+1/8)*2+1 for all n (conjectured). - M. F. Hasler, Jan 24 2017

MATHEMATICA

s = 0; k = 1; Do[ While[s = N[s + 1/k, 24]; s <= n, k += 2]; Print[k]; k += 2, {n, 1, 11}]

CROSSREFS

Cf. A002387, A056054, A091463, A091464, A091465.

Cf. also A092318, A092317, A092315, A281355, A074599, A025547.

Sequence in context: A299508 A299308 A300109 * A295758 A059849 A123853

Adjacent sequences:  A056050 A056051 A056052 * A056054 A056055 A056056

KEYWORD

nonn

AUTHOR

Robert G. Wilson v, Jul 25 2000 and Jan 11 2004

EXTENSIONS

Corrected by N. J. A. Sloane, Feb 16, 2004

More terms from Robert G. Wilson v, Apr 17 2004

STATUS

approved

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Last modified April 5 23:07 EDT 2020. Contains 333260 sequences. (Running on oeis4.)