A374359 - OEIS

A374359

a(1) = 2, a(n) = 5 for n > 1.

2, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5, 5

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OFFSET

1,1

COMMENTS

Decimal expansion of 23/9, which is an approximation of the 5th root of 109 (A374357).

Simple continued fraction expansion of (1 + sqrt(29))/14 = (1 + A010484)/14.

Also p-adic expansion of (3*p + 2)/(1 - p) for p > 5. - Stefano Spezia, May 19 2026

REFERENCES

Konrad Knopp, Theory and application of infinite series, Blackie & Son Limited, London and Glasgow, 1954. See p. 234.

LINKS

Table of n, a(n) for n=1..100.

Greg Martin and Winnie Miao, abc triples, arXiv:1409.2974 [math.NT], 2014. See p. 5.

Index entries for linear recurrences with constant coefficients, signature (1).

FORMULA

G.f.: x*(2 + 3*x)/(1 - x).

a(n) = a(n-1) for n > 2.

E.g.f.: 5*exp(x) - 3*x - 5.

Equals 10*Sum_{k>0} 1/((2*k - 1)*(2*k + 5)) [Knopp]. - Stefano Spezia, Jan 30 2026

EXAMPLE

2.555555555555555555555555555555555555555...

MATHEMATICA

LinearRecurrence[{1}, {2, 5}, 100]

CROSSREFS

Cf. A374357 (decimal expansion of the 5th root of 109), A374358 (continued fraction of the 5th root of 109).

Cf. A010484.

Essentially the same as A021022 and A010716.

Sequence in context: A240947 A023398 A374357 * A186501 A235452 A171438

Adjacent sequences: A374356 A374357 A374358 * A374360 A374361 A374362

KEYWORD

nonn,cofr,cons,easy,less,changed

AUTHOR

Stefano Spezia, Jul 06 2024

STATUS

approved