Edward Jiang - cp's OEIS frontend

A230767 Continued fraction expansion of Mertens' constant (A077761).

0, 3, 1, 4, 1, 2, 5, 2, 1, 1, 1, 1, 13, 4, 2, 4, 2, 1, 33, 296, 2, 1, 5, 19, 1, 5, 1, 1, 1, 1, 1, 12, 12, 9, 1, 8, 4, 10, 2, 1, 1, 3, 1, 1, 1, 1, 2, 2, 2, 1, 1, 1, 2, 8, 1, 4, 2, 1, 6, 1, 1, 1, 1, 1, 2, 5, 1, 3, 4, 6, 5, 1, 4, 1, 23

Offset: 0

Edward Jiang, Oct 29 2013

Charles R Greathouse IV, Table of n, a(n) for n = 0..9999

Cf. A077761 (decimal expansion).

$MaxExtraPrecision = 400; ContinuedFraction[N[EulerGamma + NSum[(MoebiusMu[m]/m)*Log[N[Zeta[m], 120]], {m, 2, 1000}, Method -> "EulerMaclaurin", AccuracyGoal -> 120, NSumTerms -> 1000, PrecisionGoal -> 120, WorkingPrecision -> 120], 71]] (* Michael De Vlieger, May 28 2015, after Jean-François Alcover at A077761 *)

a()=my(e=precision(2.>>(32*ceil(default(realprecision)*38539962/371253907)) ,9),t,s=Euler,n=1); while((t=log(zeta(n++))/n)>e, s+=moebius(n)*t); t=contfrac(s+moebius(n)*t); t[1..#t-1] \\ Charles R Greathouse IV, May 27 2015

a(19) and onward corrected by Charles R Greathouse IV, May 27 2015

Offset changed by Andrew Howroyd, Aug 08 2024

A212305 Continued fraction expansion of Pi + Euler gamma or Euler-Mascheroni Constant.

Original entry on oeis.org

3, 1, 2, 1, 1, 3, 1, 15, 1, 26, 1, 5, 3, 2, 1, 3, 3, 10, 1, 2, 1, 1, 3, 5, 1, 20, 1, 1, 2, 1, 2, 1, 1, 1, 1, 3, 6, 1, 1, 16, 3, 1, 1, 1, 1, 2, 1, 2, 5, 1, 1, 2, 2, 1, 41, 7, 2, 1, 1, 1, 7, 4, 3, 2, 2, 6, 5, 7, 7, 6, 1, 29, 5, 2, 20, 4, 1, 149, 2, 2, 1, 1, 1, 4, 13, 1, 1, 6, 15, 2, 13, 2, 1, 19, 2

Offset: 1

Edward Jiang, Oct 24 2013

PARI
```
contfrac(Pi+Euler)
```

A212316 Continued fraction expansion A074760.

Original entry on oeis.org

0, 43, 3, 2, 1, 4, 1, 1, 9, 3, 4, 1, 1, 2, 1, 14, 5, 1, 2, 7, 1, 10, 1, 4, 1, 1, 1, 2, 4, 8, 1, 274, 1, 1, 1, 4, 1, 9, 2, 1, 1, 2, 1, 1, 1, 5, 7, 2, 9, 1, 2, 9, 1, 2, 3, 153, 1, 1, 7, 2, 3, 8, 1, 12, 1, 2, 2, 113, 63, 2, 1, 1, 7, 12, 1, 5, 2

Offset: 0

Edward Jiang, Oct 24 2013

Cf. A074760.

contfrac(Euler/2 - (log(Pi))/2 - log(2) + 1)

A230581 Numbers k such that k^10 - k - 1 is prime.

Original entry on oeis.org

2, 4, 5, 6, 7, 14, 22, 25, 40, 47, 50, 57, 60, 69, 71, 76, 102, 107, 111, 114, 127, 137, 146, 152, 172, 189, 196, 197, 207, 212, 231, 251, 267, 277, 284, 291, 294, 296, 307, 309, 316, 319, 324, 371, 386, 392, 397, 412, 414, 445, 447, 467, 481, 494, 524, 527

Offset: 1

Edward Jiang, Oct 23 2013

nonn

Robert Israel, Table of n, a(n) for n = 1..10000

filter:= n -> isprime(n^10-n-1):
select(filter, [$1..1000]); # Robert Israel, May 15 2025

Select[Range[600],PrimeQ[#^10-#-1]&] (* Harvey P. Dale, Aug 20 2021 *)

for(n=1,10^3,if(isprime(n^10-n-1),print1(n,", "))); \\ Joerg Arndt, Oct 24 2013

cp's OEIS Frontend

User: Edward Jiang

A230767 Continued fraction expansion of Mertens' constant (A077761).

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A212305 Continued fraction expansion of Pi + Euler gamma or Euler-Mascheroni Constant.

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A212316 Continued fraction expansion A074760.

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A230581 Numbers k such that k^10 - k - 1 is prime.

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