cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

Showing 1-3 of 3 results.

A096731 Values of continued fraction for Pi/2 associated with the records in A096464.

Original entry on oeis.org

1, 31, 84, 116, 873, 4319, 16555, 38112, 67828, 358274, 372743, 16186423
Offset: 1

Views

Author

N. J. A. Sloane, Aug 16 2004

Keywords

Crossrefs

Cf. A096464, A053300.

A096418 Decimal expansion of Sum_{k >= 1} sin(k)/k^2.

Original entry on oeis.org

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

Views

Author

N. J. A. Sloane, Aug 16 2004

Keywords

Comments

Also, decimal expansion of the imaginary part of Sum_{k>=1} e^(i*k)/k^2. [Bruno Berselli, Mar 24 2013]

Examples

			1.013959132360768504294574338885914687561179280077717316877048512268137...

Links

Crossrefs

Cf. A096444, A096464.
Cf. A122143 (decimal expansion of Sum_{k >= 1} cos(k)/k^2).

Programs

  • Mathematica
    $MaxExtraPrecision = 128; RealDigits[ Chop[ N[ I/2*(PolyLog[2, E^-I] - PolyLog[2, E^I]), 105]]][[1]] (* Robert G. Wilson v, Aug 16 2004 *)
  • PARI
    imag(polylog(2,exp(I))) \\ Charles R Greathouse IV, Jul 14 2014

Extensions

More terms from Robert G. Wilson v, Aug 17 2004
Sequence checked by T. D. Noe, Aug 21 2006

A096475 a(n) is the smallest lesser of twin prime p, such that prime(2 + p) - prime(p) = 2n (cf. A096474).

Original entry on oeis.org

3, 17, 11, 41, 71, 101, 29, 569, 881, 137, 1151, 521, 1289, 2027, 10331, 1229, 3461, 461, 2549, 2129, 6569, 6131, 14387, 34157, 5657, 4259, 44621, 17387, 25301, 11159, 56099, 34367, 64877, 23201, 80147, 73361, 21017, 46349, 162287, 94439, 469877, 122501, 35507
Offset: 3

Views

Author

Labos Elemer, Jun 23 2004

Keywords

Links

Crossrefs

Cf. A001359, A096474, A096476.

Programs

  • Mathematica
    {ta = Table[0, {1300}], tb = Table[0, {1300}], tc = Table[0, {1300}], u = 1}; Do[s = Prime[n + 1] - Prime[n]; If[s == 2, ta[[u]] = Prime[Prime[n + 1]] - Prime[Prime[n]]; tb[[u]] = n; tc[[u]] = Prime[n]; u = u + 1], {n, 1, 10000}]; a[n_] := tc[[FirstPosition[ta, 2 n][[1]]]]; Table[a[n], {n, 3, 40}] (* Jean-François Alcover, Jul 28 2017, using Mathematica code for A096464 *)
  • PARI
    a(n) = {forprime(p=3, , if (isprime(p+2) && (prime(2+p)-prime(p) == 2*n), return (p))); p=3;} \\ Michel Marcus, Jul 28 2017
  • PARI
    list(len) = {my(v = vector(len), c = 0, q = 2, p1 = 2, p2 = 3, i); forprime(p3 = 5, , q++; if(isprime(q) && isprime(q-2), i = (p3-p1)/2 - 2; if(i <= len && v[i]==0, v[i] = q-2; c++; if(c == len, break))); p1 = p2; p2 = p3); v;} \\ Amiram Eldar, Feb 14 2025

Formula

a(n) = min{x; A096474(x) = 2n} for n = 3, 4, ...

Extensions

Name edited by Michel Marcus, Jul 28 2017
a(41)-a(45) from Michel Marcus, Jul 28 2017
Showing 1-3 of 3 results.

Started in 1964 by Neil J. A. Sloane | Maintained by The OEIS Foundation Inc.

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