A100124 -id:A100124 - cp's OEIS frontend

A039716 a(n) = prime(n)!.

2, 6, 120, 5040, 39916800, 6227020800, 355687428096000, 121645100408832000, 25852016738884976640000, 8841761993739701954543616000000, 8222838654177922817725562880000000, 13763753091226345046315979581580902400000000, 33452526613163807108170062053440751665152000000000

Offset: 1

Labos Elemer

Subsequence of A000142.

Vincenzo Librandi, Table of n, a(n) for n = 1..88

Cf. A000040, A000142, A100124, A177946.

[Factorial(NthPrime(n)): n in [1..20]]; // Vincenzo Librandi, Apr 21 2014

A039716 := proc(n)
    ithprime(n)! ;
end proc:
seq(A039716(n),n=1..10) ; # R. J. Mathar, Aug 01 2014

Table[Prime[n]!,{n,1,8}] (* Vladimir Joseph Stephan Orlovsky, Apr 27 2008 *)

a(n)=prime(n)! \\ Charles R Greathouse IV, Feb 07 2012

BB = primes_first_n(14)
L = []
for i in range(13):
    L.append(factorial(BB[i]))
L # Zerinvary Lajos, May 14 2007

a(n) = A000142(A000040(n)).
a(n) = A177946(n)*A000142(n). - Reinhard Zumkeller, May 15 2010
Sum_{n>=1} 1/a(n) = A100124. - Amiram Eldar, Nov 13 2020

A100127 Decimal expansion of Sum_{n>0} prime(n)/n!.

Original entry on oeis.org

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

Offset: 1

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 11 2004

This constant is irrational (Erdős, 1958). - Amiram Eldar, Apr 13 2020

			4.73863870268621999271779470348124955360182384664210664248096193484375408779697167489...

Paul Erdős, Sur certaines séries à valeur irrationnelle (in French), Enseignement Math. (2) 4 (1958), pp. 93-100.

Cf. A094289, A100124, A100126.

RealDigits[ Sum[ Prime[n]/n!, {n, 75}], 10, 105][[1]] (* Robert G. Wilson v, Jan 18 2015 *)

default(realprecision,100);sum(n=1,100,prime(n)/(n!),0.)

A100126 Decimal expansion of Sum_{n>0} n/(prime(n)!).

Original entry on oeis.org

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

Offset: 0

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 11 2004

			0.8591271103510884303682282623075379082585345770617761756616761775868373279803735889751322022482625639...

Cf. A094289, A100124.

RealDigits[Total[Table[n/Prime[n]!,{n,20}]],10,120][[1]] (* Harvey P. Dale, Oct 26 2015 *)

default(realprecision,100);sum(n=1,100,n/(prime(n)!),0.)

A100128 Decimal expansion of Sum_{n>0} 1/(n*prime(n)^n).

Original entry on oeis.org

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

Offset: 0

Mark Hudson (mrmarkhudson(AT)hotmail.com), Nov 11 2004

			0.5583276222317691586142791968036046951752521282087420173902229174235854763316376176520093696726521040...

Cf. A094289, A100124, A100126, A100127.

PARI
```
suminf(k=1, 1/(k*prime(k)^k))
```

A370697 Decimal expansion of Sum_{p prime} 1/p!^p.

Original entry on oeis.org

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

Offset: 0

Roberto Trocchi, Jun 07 2024

			0.25462962966981738683127573227020697042409997891314217843798476619...

Cf. A068210, A100124, A094289, A073009.

RealDigits[Sum[1/Prime[n]!^Prime[n], {n, 1, 12}], 10, 1000] // First

suminf(k=1,1/prime(k)!^prime(k)) \\ Hugo Pfoertner, Jun 22 2024

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A039716 a(n) = prime(n)!.

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A100127 Decimal expansion of Sum_{n>0} prime(n)/n!.

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A100126 Decimal expansion of Sum_{n>0} n/(prime(n)!).

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A100128 Decimal expansion of Sum_{n>0} 1/(n*prime(n)^n).

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A370697 Decimal expansion of Sum_{p prime} 1/p!^p.

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