A060746 -id:A060746 - cp's OEIS frontend

A093818 a(n) = gcd(A001008(n), n!).

1, 1, 1, 1, 1, 1, 3, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 5, 1, 3, 1, 5, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 7, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 11, 1, 1, 11, 1, 1, 1, 11, 1, 1, 11, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1

Offset: 1

Vladeta Jovovic, May 20 2004

Conjecture: every odd prime occurs as a term in the sequence.

Observation: Terms other than 1 are rare. Of the terms a(1) .. a(29524), only 187 are larger than one. Among these 187 terms, the following 50 distinct values occur: 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 121, 127, 131, 137, 139, 149, 151, 157, 163, 167, 173, 227, 257, 269, 509, 863, 919, 1049, 1331, 9409, 11881. Of these, all other are primes except 121 = 11*11, 1331 = 11*11*11, 9409 = 97*97 and 11881 = 109*109. - Antti Karttunen, Aug 28 2017

Antti Karttunen, Table of n, a(n) for n = 1..29524

Cf. A001008, A060746.

A001008(n) = numerator(sum(i=1, n, 1/i)); \\ This function from Michael B. Porter, Dec 08 2009
A093818(n) = gcd(A001008(n),n!); \\ Antti Karttunen, Aug 28 2017

More terms from David Wasserman, Apr 20 2007

Name edited (A001008 substituted for "Wolstenholme") by Antti Karttunen, Aug 28 2017

A377400 Decimal expansion of e*(gamma - Ei(-1))/2.

Original entry on oeis.org

1, 0, 8, 2, 6, 9, 1, 1, 0, 7, 6, 6, 3, 4, 6, 8, 1, 7, 9, 7, 1, 0, 4, 9, 3, 1, 7, 4, 2, 4, 6, 2, 1, 5, 2, 8, 4, 1, 9, 0, 7, 1, 0, 3, 8, 3, 8, 7, 0, 7, 2, 1, 8, 4, 5, 1, 1, 5, 0, 6, 9, 5, 8, 5, 9, 4, 7, 4, 7, 1, 2, 1, 2, 8, 9, 8, 8, 9, 9, 3, 5, 8, 9, 8, 8, 4, 6, 3, 0, 1, 7, 5, 7, 0, 7, 7, 8, 3, 7, 8

Offset: 1

Stefano Spezia, Oct 27 2024

			1.08269110766346817971049317424621528419071038...

Michael I. Shamos, A catalog of the real numbers, (2007). See p. 120.

Cf. A000142, A001008, A001113, A001620, A005843, A060746, A099285, A347952, A377401.

RealDigits[E(EulerGamma-ExpIntegralEi[-1])/2,10,100][[1]]

Equals Sum_{n>=1} (1/n!)*Sum_{k=1..n} 1/(2*k) (see Shamos).

Equals A347952 / 2.

A377401 a(n) = denominator((1/n!)Sum_{k=1..n} 1/(2k)).

Original entry on oeis.org

1, 2, 8, 72, 576, 14400, 28800, 470400, 22579200, 1828915200, 18289152000, 2212987392000, 26555848704000, 4487938430976000, 62831138033664000, 942467070504960000, 30158946256158720000, 8715935468029870080000, 52295612808179220480000, 18878716223752698593280000

Offset: 0

Stefano Spezia, Oct 27 2024

Cf. A000142, A005843, A060746, A377400.

a[n_]:=Denominator[Sum[1/(2*k),{k,n}]/n!]; Array[a,20,0]

a(n) = denominator(sum(k=1, n, 1/(2*k))/n!); \\ Michel Marcus, Oct 29 2024

Conjecture: numerator((1/n!)*Sum_{k=1..n} 1/(2*k)) = A060746(n).

cp's OEIS Frontend

A093818 a(n) = gcd(A001008(n), n!).

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A377400 Decimal expansion of e*(gamma - Ei(-1))/2.

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A377401 a(n) = denominator((1/n!)Sum_{k=1..n} 1/(2k)).

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cp's OEIS Frontend

A093818 a(n) = gcd(A001008(n), n!).

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PARI

Extensions

A377400 Decimal expansion of e*(gamma - Ei(-1))/2.

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

Mathematica

Formula

A377401 a(n) = denominator((1/n!)*Sum_{k=1..n} 1/(2*k)).

Views

Author

Keywords

Crossrefs

Programs

Mathematica

PARI

Formula

A377401 a(n) = denominator((1/n!)Sum_{k=1..n} 1/(2k)).